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

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pooja195
 one year ago
Best ResponseYou've already chosen the best response.1I would just square root both right? :P

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2difference of two squares!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now, Simplify \(\Large \frac{3x^3}{6x^2}\)

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

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2What you should do \(whenever\) you divide out anything from the denominator is to make sure the factor cannot be zero. 3 is not zero, so nothing needs to be done! But...

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You would specify that the answer is \(\frac{x}{2}\) for x\(\ne\)0

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Remember whenever we cancel a factor from the denominator, we are not allowed to cancel unless the factor is \(not\) equal to zero.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Most teachers will take half the points away if you forgot that, or some of these conditions.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2That was over copied! Simplify \(\Large \frac{x(x^2+6)}{x^2}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You cancelled x, so the condition is x\(\ne\)0

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2It's what you cancelled should not equal to zero.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2x\(\ne\)1 is for cancelling (x1)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, ready for the next one!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Simplify \(\Large \frac{p^22p+1}{p^21}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Remember to specify the conditions if you cancelled any factor.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ (p−1)(p−1) }{ p^21}\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Continue! There are factors for the denominator.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2In the worst case, use the quadratic formula!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ (p1)(p1) }{ (p+1)(p1) }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Excellent, you can now finish off. Tag on the conditions whenever you cancel!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ p1 }{ p+1 }~~~~~~~ x \neq 1\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2x\(\ne\)1 is correct, because it is the same as (x1)\(\ne\)0

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2is that clear how we got x\(\ne\)1 ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2This is going to be all of these for the rest of 11! Just one more of these simple ones. Once you can do the simple ones, you'll even like the more complicated ones! lol Simplify \(\Large \frac{3(4m)}{6(m4)}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2you get the idea, but a little too fast ! :(

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Remember m4 = (4m), and 3/6=1/2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2... and the conditions!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Well, we have \(\Large \frac{3(4m)}{6(m4)}\) = \(\Large \frac{3(m4)}{6(m4)}\) =\(\Large \frac{3(m4)}{3*2(m4)}\) so we cancel 3 and (m4) but we know that 3\(\ne\)0, so we don't have to specify as a condition, the other one is m4\(\ne\)0. If we add 4 to each side, we have m\(\ne\)4

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So the final answer is 1/2, where m\(\ne\)4

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2are we good, especially with conditions? We'll be working with conditions and factorization throughout ch. 11

mathmate
 one year ago
Best ResponseYou've already chosen the best response.234. simplify \(\Large \frac{x^29}{x^25x6}\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ (x+3)(x3) }{ (x6)(x+1)}\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2anything else to do or to write?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2(note: the factoring is correct! Welldone!)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2If you did not cancel anything, then you make a note: the expression is already in its simplest form. (and no conditions if nothing cancelled)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Simplify if possible \(\Large \frac{3x5}{2530x+9x^2}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Remember steps for factoring: 1. take out GCF (common factors) 2. Check if it is difference of 2 squares (Must be a difference, and only has two terms) 3. Check if it is a perfect square: First and last terms are perfect squares, and middle term is twice the product of the squareroots of the two end terms. Example: a^2+2ab+b^2 : End terms are perfect squares, middle = 2(a)(b), so yes, this is a perfect square, equal to (a+b)^2. 4. Try factoring.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.21. any common factors (in the denominator)?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.22. Is it diff. of 2 squares?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.23. Is it a perfect square?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Hmm, let's see. Squareroot of first term = sqrt(25) =5 squareroot of last term =sqrt(9x^2)= 3x (so far so good, both terms are perfect squares)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now do a foil on (53x) and see if the middle term fits. (53x)(53x)=5^215x15x+9x^2=5^230x+9x^2 Yay, so it's a perfect, equal to (53x)^2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So now can you complete it?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Shall we go back to perfect squares?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ 1 }{ 3x5 }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Watch out: 53x = 1 (3x5) and also since we cancelled 3x5, we specify the condition x\(\ne\)5/3

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2For perfect squares, it has to satisfy 3 conditions 1. end terms are perfect squares, i.e. you can find the square roots without leaving the radical. 2. middle term equals twice the squareroots of the end terms. 3. the middle term has the same sign of the factored terms.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2We check that with an example Factor 81x^2 xy +64y^2.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Note that condition one means that both end terms must be positive. Here first term = 81x^2, square root = 9x

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Last term = 64 y^2, squareroot = ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2@pooja195 What is the squareroot of the last term?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Last term = 64 y^2, squareroot = ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Good. What's twice the product of the squareroots?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2We need to multiply together the squareroots (of the first and third terms), and double it.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2the square roots are 9x and 8y,so the product is 72xy, and doubling it shoud give 144xy. This should match the middle term (if the expression is a perfect square). It doesn't because I forgot to fill in the 144 in the middle. So we conclude that (9x+8y)^2=81x^2+144xy+64y^2=(9x+8y)^2.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433718072207:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433718524311:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So if we are given 81x^2+144xy+64y^2 We can do the reverse of FOIL, assuming that it is a perfect square. We find 9x by sqrt, and 8y by sqrt. Then we test if 2(9x)(8y)=144xy, if it's equal (9x+8y)^2 are the factors.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433718696561:dw

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Thats so much more better :)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1I understand this a bit more :o

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Good! An image is worth 1000 words, I was told!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So we'll be back on track!?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.211.4 Multiplying and dividing rational expresssions =================================================== calculate \(\Large \frac{6}{15}\times \frac{12}{9}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I would like you to treat the numbers as products of factors, and see if you can simplify without the calculator.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1i cant do it without a calc! :O

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2It's not the answer we want, just the process. I'll do that for you.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\Large \frac{2.3}{3.5}\times \frac{2.2.3}{3.3}

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\(\Large \frac{6}{15}\times \frac{12}{9}\) =\(\Large \frac{2.3}{3.5}\times \frac{2.2.3}{3.3}\) now cancel factors =\(\Large \frac{2}{5}\times \frac{2.2}{3}\) =\(\Large \frac{8}{15}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2If you replace each prime factor (2,3,5,...) by a polynomial, this is exactly what we do to multiply rational expressions!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2simplify \(\Large \frac{x}{3x^29x}\times\frac{x3}{2x^2+x3}\) [do not forget the conditions whenever you cancel]

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ (x3) }{ 3(x−1)(2x+3)(x−3) }\]

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ 1 }{ 3(x1)(2x+3) }\] x/= 3

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Almost. The last step is all correct. There was a mistake in the first step:

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Oh, actually, you were right, I was wrong. The final answer is good! Congrats!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Do you still remember how to do a division of fractions?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I'd say: flip the fraction after the \(\div\) sign.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Can we keep doing multiplication ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Sure! Another one coming up

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\(\Large \frac{c^264}{4c^3} \times \frac{c}{c^2+9c+8}\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ (c+8)(c−8) }{ 4cc(c+1)(c+8) }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Remember you cancelled a "c" already. Keep track of that.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Can you finish it off ;;

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\(\Large \frac{c^264}{4c^3} \times \frac{c}{c^2+9c+8}\) =\(\Large \frac{(c+8)(c8)}{4c^3} \times \frac{c}{(c+8)(c+1)}\) cancel c and (c+8) =\(\Large \frac{(c8)}{4c^2(c+1)}~~~ x\ne 8,0\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Is the last part ok for you now?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Another multiplication?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Division: \(\Large \frac{1}{2}\div\frac{1}{5}\) =\(\Large \frac{1}{2}\times\frac{5}{1}\) Is this familiar to you?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2We would do the same with rational functions.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Gimme a second to type it up.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2simplify \(\Large \frac{x}{x+6} \div \frac{x+3}{x^236}\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ x }{ x+6 }\times \frac{ (x+6)(x6) }{( x+3) }\] \[\frac{ x(x6) }{ (x+3) }~~~~~x \neq6\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Perfect!!!! Can't be better!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1I did that without a calc :O

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Oops, what about the previous ones ! LOL

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Simplify \(\Large \frac{45x^39x^2}{x} \div \frac{6(x5)}{2}\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ 3x(5x−1) }{ x5 }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Wow, what did you eat for supper?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1No i have this : ) next case!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.211.5 Adding and Subtracting with like denominators =================================

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Like denominators mean that the denominators are either the same, or just a simple multiple.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So it's a matter of adding the numerators, like:dw:1433721592963:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Add \(\Large \frac{x+2}{x} + \frac{3x2}{x}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2...and the next step is...

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1the answer would be 4

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Because the x's cancel right?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2x\(\ne\)0 "conditions whenever cancelling a factor in the denominator".

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\(\Large \frac{3x4}{x4}  \frac{2x}{x4}\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1i knew it was coming :P \[\frac{ 1x4 }{ x4}\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The conditions are the only difficult part in these examples!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433722130469:dw

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1multiplication right?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Nope, perimeter would be the sum of all four sides.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2We only have two more cases.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1I dont like this one ;;

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1im not even sure where to start ..

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433722487080:dw

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge~\frac{ 2(x−2)(x^3+4x^2−12x+4) }{ (x+2)(x−2)(x−2) }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2wow, not like that. The addition had already been done, because the denominators are the same.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2All you need to do is to cancel (x2) and give the answer!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433722913558:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Do you see what was happening? I multiplied by 2 because the opposite sides are identical. I then add them, using the common denominator that we are given with. Did the additions to come to 2(x+4)(x2)/(x2) Since (x2) is a common factor, we can cancel as long as x2\(\ne\)0, or x\(\ne\)2 So the answer is 2(x+4), with x\(\ne\)2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, next case: 11.6 adding and subtracting rational functions ith unlike denominators ============================================= It's almost the same as 11.5. It's just you need to do dancing class with the denominator before adding and subtracting.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2example Find common denominator of \(\Large \frac{1}{12x} +\frac{2+x}{40x^4}\) The common denominator can be found similar to the dancing class: dw:1433723859840:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Once you can find the common denominator readily, rest is relatively straightforward.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So that's good, we'll proceed with an example.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Simplify \(\Large \frac{x+1}{5} + \frac{2x}{6}\) Can you first try to find the common denominator?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433726621112:dw