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pooja195
 one year ago
@mathmate
pooja195
 one year ago
@mathmate

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mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Yep. Do you know direct and inverse variation?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Direct variation is a function that varies directly with x. For example X Y 1 2 2 4 3 6 4 8 5 10 is a direct variation. Notice that Y/X is always the same ratio (of 2). so far so good?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2On a graph, direct variation is a straight line passing through the origin. dw:1432866053517:dw Here f1(x), f2(x), f3(x) are all direct variations, but g(x) is not, because it does not pass through the origin.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2For inverse variations, they work differently. Y is the inverse (or reciprocal) of x. This way, X*Y is a constant (same number). Example: X Y 1 2 2 1 3 2/3 4 1/2 5 2/5 6 1/3 ... notice the product of X*Y is always 2. the graph looks like this dw:1432866347703:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok for inverse variation?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Can we move on the rational expressions?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2A rational expression is a polynomial divided by another polynomial.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Example, (5x+3)/(2x+1) is a rational expression.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The sum of two rational expressions is also a rational expression, just like the sum of two fractions is still a fraction.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Even with one single rational expression, we can simplify , for example, what would be \(\large \frac{(4x+3)(x1)}{(x1)}\) ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Before you do foil, did you notice anything?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Yes, only as long as (x1) does not equal zero!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So we say: \(\large \frac{(4x+3)(x1)}{(x1)}=4x+3\) if x\(\ne\)1

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So far, we've been lucky. Both the numerator and denominator contained (x1) as a common factor. What if we are given the following to simplify: \(\large \frac{4x^2x3}{x1}\) ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2We cannot tell offhand if there is any common factor, so what do we do?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0We use the wheel thingy

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Good, or "factorize" is the other word for the wheel thingy! Can you do that, please?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0dw:1432867194095:dw \[(4x^24x)+(3x3)\] \[4x(x1)+3(x1)\] \[(4x+3)(x1)\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Excellent! Now you replace the numerator of the rational expression with what you've got, what do you get? \(\large \frac{4x^2x3}{x1}= ?\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ (4x+3)(x1) }{ (x1) }\] (x1) cancel out. Final answer: \[ \huge 4x+3\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Whenever you cancel out in a rational expression, you need to ADD a condition that what you cancel out is not zero, so you need to add x\(\ne\)1 (or x1\(\ne\)0).

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2We don't do that in fractions because we almost always work with nonzero factors. If we had a fraction 5*0/4*0, cancelling the common factor 0 would give 5/4 as the answer, which is not the same as 0/0.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So the answer is again 4x+3 with x\(\ne\)1.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Yes, it complicates life a little, but that's the only difference from fractions.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So whenever you need to simplify a rational expression, factorize as much as you can, and cancel as much as you can. Add one condition whenever you cancel a factor (unless the same factor appears twice) Example: (x+3)(x+1)^2/((x+1)^2(x+5)) =(x+3)/(x+5) if x\(\ne\)1

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Are we good so far (except you don't like the condition! :) )

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2If we multiply rational functions, it's the same as in fractions. Again, if we cancel, we need to specify conditions! \(\large \frac{x+5}{x2} * \frac{x2}{x+3} = \frac{x+5}{x+3} \) if x\(\ne\)2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2For divisions, it's the same as in multiplication, except that we need to flip the divisor and multiply. Example: \(\large \frac{x+5}{x2} \div \frac{x+5}{x+3} = \frac{x+5}{x2} * \frac{x+3}{x+5} =\frac{x+3}{x2}\) if x\(\ne\)5

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now for adding and subtracting with like denominators, it would be just like in fractions. Should I give an example anyway?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0Can we just skip those :P i know those

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2What about with unlike denominators, are you ok with those?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok. But back to those with like denominators: after adding or subtracting, you will still need to factorize and look for factors to cancel AND add a note/condition. Is that ok?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Ok, now +/ expressions with unlike denominators. Just like 1/3+2/5 common denominator is 3*5=15 so we'll make equivalent fractions before adding = 5/15 + 6/15 now add =11/15 ok?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now for rational exprssions: \(\large \frac{x+1}{x2}\frac{x2}{x+4}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2What would be the common denominator? (do not FOIL, otherwise we need to factorize afterwards.)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2We need the product of the two denominators, (x2)(x+4), so that we can make equivalent expressions. \(\large \frac{x+1}{x2}\frac{x2}{x+4}\) =\(\large \frac{(x+1)(x+4)}{(x2)(x+4)}\frac{(x2)(x2)}{(x+4)(x2)}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2To this we have to add the conditions that x2\(\ne\)0 and x+4\(\ne\)0

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok so far in making equivalent fractions?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The rest of it is adding two rational expressions with like denominators. After addition/subtraction, you need to factorize and cancel expression (and add conditions if applicable).

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0im so confused and lost T_T

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Yesterday we went through 11.2 to 11.6. Now it's time to do some practice!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Just kidding, sure, later!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2@pooja195 Time to work!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0Just remebered i have a thing to do.... oops cant work :P

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Ok, I'll grab you later, ok?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0BWAHAHAHA XDDD :3 yr so innocent xS

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0im free :# we can math :P

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Want a practice to make sure?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2BTW, were the correct answers in the quiz all between 11.2 and 11.3?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So you did get some in other sections, that's good!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now try to simplify: \(\large f(x)=\frac{x^2+x6}{x^2x12}\) Do not forget to mention the condition, if any

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0i thought i did great on it but i ended up failing

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0;; can we start with something easier :(

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Ok, simplify \(\large f(x)=\frac{x^2+x6}{(x+3)(x4)}\) :)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0dw:1432933988455:dw IDK T_T

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Remember, when the product (6) is negative, the two numbers you're looking for have different signs. Does that help?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1432934285205:dw Which pair works?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Exactly. Are you able to complete the answer now?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ (x2)}{ (x+4) }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Almost, just a transcription error (should be x4 at the bottom) AND missing very important information... Do you know what's missing?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The condition that (x+3)\(\ne\)0. Teachers are waiting to jump on that! :(

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So the complete answer is (x2)/(x4) with x\(\ne\) 3

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0ye the rest is fine :)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Just have to remember that whenever you cancel a term, it comes with a condition. Like when you buy candies, you always pay! :)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Want another one similar?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, here's another one. Notice that the numerator is the same as the previous, so you are allowed to reuse your own work this time. Simplify \(\large \frac{x^2+x6}{x^22x15}\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0dw:1432935523037:dw \[\frac{(x2)(x+3) }{ (x5)(5+3)}\] Final answer \[\frac{ (x2) }{ (x+5) }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Remember the last problem? transcription and something missing???

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0T_T i dont know this!!! >:(

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Good up to this: \(\frac{(x2)(x+3) }{ (x5)(x+3)}\) After that, the final answer after cancelling is \(\frac{(x2)}{ (x5)}\) with the condition that x\(\ne\)5.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2All you have to remember is if you get candies, you pay!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Sorry, we have to stick to rules! Now can you simplify (x2)(x+4)/(x+4) ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You cancelled (x+4) right?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So we write (x2).....

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You were close: (x2) for x\(\ne\)2 is the complete answer.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, let's try another: simplify (x4)(x+2)/(x4)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Almost, it would be (x+2) for x\(\ne\)4 because if x=4, the expression/function is 0/0, and that does not have a value. So our answer of (x+2) is valid as long as x\(\ne\) 4

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now try this: simplify (2x+5/2)(x+3)/(2x+5/2)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0No no more of these T_T

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I am looking forward to see you do one completely by yourself, because I won't be there to help you when you do your quiz!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The answer is (x+3) for 2x+5/2\(\ne\)0 Remember when 2x+5/2=0, the expression becomes 0/0 and is undefined. So to avoid this situation, we specify that 2x+5/2\(\ne\)0

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0Can we please skip these T_T

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Sorry, math is a cumulative knowledge. If we don't do it right, all the following topics will be wrong! I am asking you to show me at least once that you will follow a cancellation with a condition.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Simplify (2x+3)(x1)/(x1)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2yes, put if, for, for all, or whenever... to indicate that it is a condition. so 2x+3 for all x\(\ne\) 1

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I will skip this step and move on to 11.4. But remember that in all the other topics, whenever you cancel, you still have to write the condition, else the answer is wrong without it. Are we good?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.211.4 is on rational expressions and not radical expression, I suppose. Can you confirm?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0yea lol rational is right

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, try this: simplify \(\large \frac{x2}{x+3}\times\frac{x+3}{x4}\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0(x2)(x+3)/(x+3)(x4) \[\huge \frac{ x2 }{ x4 }\neq 3\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2That's the idea! We write the condition separate though, \(\large \frac{ x2 }{ x4 }\ for\ all\ x\neq 3\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2correction: \(\large \frac{ x2 }{ x4 }\ for\ all\ x\neq 3\) because we don't want x+3=0

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now, try Simplify \(\large \frac{x2}{5x+6}\times\frac{2x3}{x2}\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0(x2)(x2)/(5x+6)(2x3) T_T Lets do a diffrent one! :

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You need to cancel the (x2) at the top with the (x2) at the bottom, the will give (2x3)/(5x+6) for all x\(\ne\) 2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok try this: Simplify \(\large \frac{x^25x+6}{5x+6}\times\frac{5x+3}{x2}\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0(x3)(x2)(5x+3)/(5x+6)(x2) \[\frac{ (x3)(5x+3) }{ (5x+6)(x2) }\neq2\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2you cancelled the x2 at the bottom, so x2\(\ne\)0, or x\(\ne\)2 The answer will then read: \(\frac{ (x3)(5x+3) }{ (5x+6)} \ for\ all\ x\neq2\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Simplify \(\large \frac{x3}{5x+6}\div \frac{x2}{5x6}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You'll need to invert the second term to change division to multiplication: =\(\large \frac{x3}{5x+6}\times \frac{5x6}{x2}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2oops the question is wrong. It is meant to have 5x+6 top and bottom! \(\large \frac{x3}{5x+6}\div \frac{x2}{5x+6}\) =\(\large \frac{x3}{5x+6}\times \frac{5x+6}{x2}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now we cancel the common factor 5x+6 (as long as 5x+6\(\ne\)0. so we write =\(\large \frac{x3}{x2}\) for all 5x+6\(\ne\)0 =\(\large \frac{x3}{x2}\) for all x\(\ne\)6/5

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2@pooja195 we were at 11.4 are you ready?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2It seems better now. Are you good with multiplication and division of rationals?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, we'll go through all sections, and then come back to those which you feel wobbly. BTW, do you have some examples from school, we can work on those.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0yeah lol my hoe work ill put up a problem from that : )

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Sure! It will be less boring.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0xD \[\frac{ x^2+2x15 }{ 3x^2+6x }\div \frac{ 3x^29x }{ x^2+7x+10 }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So what would be your first step?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2That's ok, but I would prefer to put the second term upside down, so we will always working with multiplication.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\(\frac{ x^2+2x15 }{ 3x^2+6x }\div \frac{ x^2+7x+10 }{ 3x^29x }\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Oops too small, but I can still read it.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0lol ok so now we factor right?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2right, lemme fix the div sign, but you can go ahead and factor. Remember the first step is to take out the common factors of each expression, ex. in 3x^2+6x. Take out 3x.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\(\large \frac{ x^2+2x15 }{ 3x(x+2) }\times \frac{ x^2+7x+10 }{ 3x^29x }\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0Ok this is the part where i get kinda confused....you know how theres like two seperate equations on top? They both can be factored but how would i write it out?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Actually on second look, would the original question be a multiplication instead of a division?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You can start with writing them separately in two separate numerators. After that, we cancel.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2But it seems that there is not much to cancel unless the original question was a multiplication.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Sorry, I take it back. There is at least one that we can cancel.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So you can go ahead and factor, as though they are two separate terms. We can combine them after cancelling.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I mean you can proceed with this: \(\large \frac{ x^2+2x15 }{ 3x(x+2) }\times \frac{ x^2+7x+10 }{ 3x^29x }\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0How would i write out the factors?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The bottom one on the right should take out 3x as well, so you put \(\large \frac{ x^2+2x15 }{ 3x(x+2) }\times \frac{ x^2+7x+10 }{ 3x(x3) }\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2For the ones in the numerator, you can put them where they are now.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2If you want, we can factor the left numerator together.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\(\large x^2+2x15\) =\(\large (x \ )(x+ \ )\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0ok dw:1433012589434:dw dw:1433012632806:dw \[\frac{ (x+5)(x3) }{ 3x(x+2) } \times \frac{ (x+5)(x+2) }{ 3x(x3) }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Good job! Speed of a bullet!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2can you now post me the factors that you can cancel, and write down the condition associated with each one?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2like: (x3) means x\(\ne\)3

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You can write all the factors on top as one single numerator, and similarly for the denominators. Looks like this:

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ (x+5)^2 }{ 3x }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Yes, but there are two "3x" , so you write 9x^2 at the bottom.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2...and don't forget to add the 2 conditions that correspond to the two factors that you cancelled out.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[x \neq3~~~~~~~x \neq2\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2yes. Please write the answer with the conditions on one line, the conditions are "and" because both have to be satisfied.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2If you want to see how it should be done, see the example near the bottom of the page: http://www.purplemath.com/modules/rtnlmult.htm

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0Does it have to be written like that? :/

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2It would be the simplest, simpler than what I would have done.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ (x+5)^2 }{ 3x },x \neq2,x \neq3\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2That's ok too, but do remember it's 9x^2 at the bottom, because we had two 3x left at the bottom!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\(\large\frac{ (x+5)^2 }{ 9x^2 },x \neq2,x \neq3\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Excellent, you got one done, and it wasn't a simple one like my (boring) ones.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Got other ones to try?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge \frac{ x^264 }{ 3x^3 }by~(88)\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Sure it's (88) ? (equals zero!) O_o!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge \frac{ (x+8)(x8) }{ 3x^3}\div \frac{ 1 }{ (x8) }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Ok! I think you did the division twice (you flipped, and you kept the division sign!)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Is it \(\huge \frac{ (x+8)(x8) }{ 3x^3}\times \frac{ 1 }{ (x8) }\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2And you factored the top rightaway, ;) ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2What's your answer then?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Bet you this one comes out in the quiz.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge\frac{ 1(x+8) }{ 3x^3 },x \neq 8\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Another one done, with 100%.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2yes please! More, more....

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I like your examples better, they are less boring.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Simplify \(\large \frac{x^2+6x+9}{x^29}.\frac{3x9}{x^2+2x3}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2There is no grouping to be done in the factoring because the coefficients of the quadratic expressions are all one (1).

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ (x+3)(x+3) }{ (x+3)(x3) }\times \frac{ 3x9 }{x+3)(x1) }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Did you use the perfect square and diff. of two squares?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2or you factored all three?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0Diffrence of square \[\huge \frac{ (x+3)(x+3) }{ (x+3)(x3) } \times \frac{ 3(x3) }{ (x+3)(x1) }\] not sure how to do the next part

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Excellent. Now you cancel, and note the conditions as you cancel.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2(x3) and (x+3)^2 will be cancelled top and bottom, leaving \(\large \frac{3}{x1}\), x\(\ne\)3,1

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2* \(\large \frac{3}{x1}\), x\(\ne\)3,3 You don't have to worry about x+3 twice.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Simplify \(\large \frac{2x^2+x6}{x^22x8} \div \frac{2x^2x3}{x^23x4}\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ (2x3)(x+2) }{ (x4)(x+2) }\times \frac{ (2x3)(x+1) }{ (x+4)(x1) }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Great, just you need to flip, and I think bottom left should read (x4)(x+1) before flipping.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2That was a great piece of work, involving 4 factorizations,, out of which you got 3 of them perfect, and one was just a switch of the sign! :)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0wait so what should it look like :. ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The answer should be very simple, almost the simplest possible, plus three conditions.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\(\large \frac{ (2x3)(x+2) }{ (x4)(x+2) }\times \frac{ (x4)(x+1) }{ (2x3)(x+1) }\) Can you finish it?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0all of them cancel out! T_T

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2That's good, so what's the answer? (it's not zero).

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge x~\neq4~~~x~\neq2~~~~~x~\neq1~~~~~????\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Almost, compare 5/5=1 x4\(\ne\)0 means x\(\ne\)4, etc. so \(\large 1, x\ne 2,1,3/2,4\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Continue with these "easy" ones, or some addition?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0i wanna move onto something more challenging :)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Like addition and subtration?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, Simplify \(\large \frac{4}{x^216}+\frac{3}{x^2+8x+16}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Step 1: factorize, then we can find the lowest common multiple (LCM)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2or the common denominator.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge \frac{ 4 }{ (x+4)(x4) }+\frac{ 3 }{(x+4)(x+4) }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2now we have on denominator (x4)(x+4) and the other (x+4)(x+4). Can we find the common denominator? Example: common denominator of 6 and 9: 6=2*3, 9=3*3, so common den. = 2*3*3 the common denominator contains all the factor of each of the originals.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2x+4 does not contain x4, and x+4 twice. Hint: the common denominator here has three factors.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2(x1)(x+4)(x+4) contains (x1)(x+4) which is the first one, and also contains (x+4)(x+4) the second one. So (x1)(x+4)(x+4) is the common denominator. You can also get it by multiplying together the two denominators, but cancelling one of the repetitions. \((x4)\color{red}{(x+4)} (x+4)\color{red}{(x+4)}\) We will keep only one of the two reds because they repeat. That gives \((x4)\color{red}{(x+4)} (x+4)\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now step 2: For the first term, we need to multiply top and bottom by (x+2) to get the bottom to be the common denominator, i.e. \(\large \frac{4\color{blue}{(x+4)}}{(x4)(x+4)\color{blue}{(x+4)}}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Similarly for the second term: \(\large \frac{3\color{blue}{(x4)}}{\color{blue}{(x4)}(x+4)(x+4)}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Since we have a common factor, we can now add: \(\large \frac{4(x+4)}{(x4)(x+4)(x+4)}+\frac{3(x4)}{(x4)(x+4)(x+4)}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2= \(\large \frac{4x+16+3x12}{(x4)(x+4)(x+4)}\) = \(\large \frac{7x+4}{(x4)(x+4)(x+4)}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2and that's the answer.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Did you follow all the steps?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2If you get stuck, tell me where.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You can also read example 4 of the following link: http://www.cliffsnotes.com/math/algebra/algebraii/rationalexpressions/addingandsubtractingrationalexpressions

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2For the common denominator part, I will rephrase as follows: You can also get it by multiplying together the two denominators, but cancelling one of the repetitions, if any, \(between\) the denominators. \([(x−4)\color{red}{(x+4)}] [(x+4)\color{red}{(x+4)}]\) We will keep only one of the two reds because they repeat. That gives \((x−4)(x+4)\color{red}{(x+4)}\) as the common denominator.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The next step is to make equivalent fractions by multiplying by appropriate factors to make the denominator the common denominator. This is done for each term to be added/subtracted.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Do you have anything from your school notes?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Example or exercises?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, shall we take a break/

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0mmmmmmmmmmmmmmmm k :)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Do you have some examples for the easy ones (like denominators)?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0No. I'd prefer you give the problems... :/

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Simplify \(\large \frac{4x+3}{x^216}+\frac{3x+4}{x^216}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The terms already have a common denominator, so we just add the numerators: \(\large \frac{4x+3\ \ +\ \ 3x+4}{x^216}\) Can you finish it?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{7\left(x+1\right)}{\left(x+4\right)\left(x4\right)} \]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Simplify \(\large \frac{x^23x+2}{2x4}\frac{x1}{2x4}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Like the one before, the two terms already have a common denominator, so just do the subtraction of the numerators and factor, if possible, the difference.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{\left(x3\right)\left(x1\right)}{2\left(x2\right)} \]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Oh yes, I thought the difference is not factorable! lol Great job!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\(\large \frac{2x+3}{x^2+4x+4} +\frac{x^2+2x+1}{(x+2)^2}\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0;; not this one! Lets skip it! :D

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2lol, don't get fooled! The two denminators are actually identical, if you factor the first or expand the second, you will find that they are the same. Just add the numerators and factor if necessary.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge\frac{ 2x+3}{ (x+2)(x+2)}+\frac{ (x+1)(x+1) }{ (x+2)(x+2) }\]

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge\frac{ 2x+3(x+1)^2}{ (x+2)(x+2) }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Watch out: \(\huge\frac{ 2x+3\color{red}{+}(x+1)^2}{ (x+2)(x+2) }\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Keep going, you're almost there!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You need to expand the (x+1)^2 using FOIL or identities and then add.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 2x+3+x^2+1x+1x+1 }{ (x+2)^2}=\frac{ x^2+4x+4 }{ (x+2) }=\frac{ (x+2)(x+2 }{ (x+2)(x+2)}\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Great! So after cancelling you have a numeric answer with a single condition:

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The answer is 1 (5*5/(5*5)=1) and the condition is x+2\(\ne\)0, or x\(\ne\)2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Remember we don't want what we cancelled to be zero.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Try the unlike denominators now or later?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I'll start with this: Add \(\large \frac{2}{9}+\frac{7}{12}\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0No lets skip this section i dont like this section

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, 9=3*3, 12= 3*4 Let's find the LCM: dw:1433023297993:dw so \(\large \frac{2}{9}+\frac{7}{12}=\frac{2*4}{9*4}+\frac{7*3}{12*3}=\frac{8}{36}+\frac{21}{36}=\frac{29}{36}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2hold on! have to find the question!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0ugh no i put everything away ;; lets just use yours :(

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0mathmate i thin your pm's are lagging

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2forget the previous one with the wrong operator. Simplify \(\large \frac{2x^2+x6}{x^22x8}\div \frac{2x^2x3}{x^23x4}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\(\large \frac{2x^2+x6}{x^22x8}\times \frac{x^23x4}{2x^2x3}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Next, factor, one piece at a time, and show intermediate steps, please!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge \frac{ 2x^2+x6 }{ x^22x8 }\times \frac{ x^23x4 }{ 2x^2x3 }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I would do it like that: For the top left, we have 12 and +1. We know 3*4=12 with a difference of 1 (diff because 12 is negative). So figure out the right signs, and that will be +4 3 (to give +1).

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[huge(x+4)(x3)\] \[\huge(2x^2+4x)(3x6)\] \[\huge2x(x+2)~~~~~3(x+2)\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Then proceed with grouping: 2x^2+4x 3x6 = 2x(x+2) 3(x+2) = (2x3)(x+2)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Good job, continue please!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0[\huge \frac{ (2x3)(x+2) }{ (x4)(x+2) }\times \frac{(x4)(x+1) }{ 2x^2x3 }\]

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[(2x^2+2x)(3x3)\] \[2x(x+1)~~~~~~~3(x+1)\] \[(2x3)(x+1)\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You mean \[\huge \frac{ (2x3)(x+2) }{ (x4)(x+2) }\times \frac{(x4)(x+1) }{ 2x^2x3 }\]

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[[\huge \frac{ (2x3)(x+2) }{ (x4)(x+2) }\times \frac{(x4)(x+1) }{ (2x3)(x+1) }\] \]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now the finishing touch!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2right, but not finished yet!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0omg no T_T the conditions

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The conditions can be obtained by equating each factor cancelled to zero. Ex. 2x3\(\ne\)0 means x\(\ne\)3/2, etc.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Didn't your teacher ask you to specify the conditions, or is it just I?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0no he doesnt make us list those :/

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Even in the quiz? Is it multiple choice?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Ok, do it just for this one,to remind you that they should be there. After that, if they are listed correctly, you don't have to do it until after the quiz!!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So the four conditions are: 2x3\(\ne\)0 x+2\(\ne\)0 x4\(\ne\)0 x+1\(\ne\)0

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[x \neq 3/2~~~~~x \neq2~~~x \neq4~~x \neq1\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So you can write them together as: x\(\ne\)2,1,3/2,4

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Excellent, thank you! :)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Ready for another one, simpler, and no conditions!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\(\large \frac{4+2x}{x^24}.\frac{x^24x+4}{x2}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Hint: x^24 is the same as x^22^2, difference of 2 squares.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 4+2x }{ (x+4)(x4) }\times \frac{ (x2)(x2) }{(x2) }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2and x^24x+4 is a perfect square, if you recall!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You can do better with the first expression (on the left, both top and bottom.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Remember bottom was x^22^2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2good, 2+x= x+2 We usually write polynomials in decreasing power. This way it's easier to find like terms.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The bottom is (x+2)(x2)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I think it's 2. Can you check?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Good. Want to do rational addition/subtraction (more difficult) or rational equations?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0None of the above. xD

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, it's getting late!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.0LOL ok we can continue tommzzz
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