What is the simplified form of x plus 1 over x squared plus x minus 6 ÷ x squared plus 5x plus 4 over x plus 4 ? 1 over the quantity x plus 3 times the quantity x plus 4 1 over the quantity x plus 3 times the quantity x minus 2 1 over the quantity x plus 4 times the quantity x minus 2 1 over the quantity x plus 3 times the quantity x plus 1

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What is the simplified form of x plus 1 over x squared plus x minus 6 ÷ x squared plus 5x plus 4 over x plus 4 ? 1 over the quantity x plus 3 times the quantity x plus 4 1 over the quantity x plus 3 times the quantity x minus 2 1 over the quantity x plus 4 times the quantity x minus 2 1 over the quantity x plus 3 times the quantity x plus 1

Mathematics
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\[\frac{ x + 1 }{ x^2 + x -6 } \div \frac{ x^2 + 5x + 4 }{ x + 4 }\] @satellite73

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http://www.wolframalpha.com/input/?i=%28x%2B1%29%2F%28x^2%2Bx-6%29*%28x%2B4%29%2F%28x^2%2B5x%2B4%29
you go that right?
nice use of the equation tool btw
i can show you another trick in using wolfram
okay and heres the question
simplify (12z^2 - 25z + 12)/ (3z^2 + 2z - 8)
using the link i got (4z - 3)/(x + 2)
ok i so take what you wrote, copy and paste it directly in to wolfram
yeah i did that and got (4z - 3)/(x + 2)
yeah i get that too, but of course with a z
i could also show you how to do it without wolfram, it is "factor and cancel"
oh yeah typo lol sorry okay i think it'll be better without wolframe alpha in case my teacher asks
ok then here is the deal do you know how to factor?
sometimes but not really it'll be helpful if you showed me though
i don't actually, believe it or not if i wanted to factor i would cheat
what i mean is that i have no good way to show you how
i usually use a site for factoring
that works, of course wolfram will do that too
so in case the teacher asks, you can say something like this ;
\[ (12z^2 - 25z + 12)=(4 z-3) (3 z-4)\] and \[(3z^2 + 2z - 8)= (3 z-4) (z+2)\]
so \[\frac{12z^2+25z+12}{3z^2+2z-8}=\frac{4z-3)(3z-4)}{(3z-4)(z+2)}\]
oh and then you cross out (3z - 4)?
there is a common factor top and bottom of \(3z-4\) which cancels, you get \[\frac{(4z-3)(3z-4)}{(3z-4)(z+2)}=\frac{4z-3}{z+2}\]
exactly what you said
that is the idea of all of these factor and cancel
okay cool i get it now
as to how to factor, you are pretty much on your own, but you can use wolfram to do it for sure
okay thnx
and you can use wolfram to give the final answer too, but once you have it factored it is easy to cancel
ill also ask someone else on os
want to try another one ?
yeah
ok i get a cup of coffee, you post
ok What polynomial identity should be used to prove that 21 = 25 - 4?
wow do you have any choices? \(21=25-4\) is simple arithmetic
What polynomial identity should be used to prove that 21 = 25 - 4? Difference of Cubes Difference of Squares Square of Binomial Sum of Cubes
ooh ok
25 and 4 are two squares
then B?
\[25=5^2\] and \[2^2\] so yeah B
what a dumb retricequestion next?
thnx
given the parent function of f(x) = x3, what change will occur when the function is changed to f(x - 3)? Shift to the right 3 units Shift to the left 3 units Shift up 3 units Shift down 3 units
when you subtract inside the function it move is 3 units to the RIGHT
thnx
ased on the table of values below, find the slope between points where x = 1 and where x = 4. x y 1 8 3 6 4 −1
what is the corresponding y value when x = 1?
ok ok
8
\[\frac{-1-8}{4-1}\] is whatyou have to compuote
i get \[\frac{-9}{3}=-3\]
thnx
yw
how many more?
a couple Which of the following expressions is the conjugate of a complex number with 2 as the real part and 3i as the imaginary part? 2 + 3i 2 − 3i 3i + 2 3i − 2
the conjugate of \(a+bi\) is \(a-bi\)
so b?
the conjugate of \(2+3i\) is \(2-3i\) that was an easy one
yeah b
okay thnx
yw next?
Two car washers, Michelle and Nancy, are working on your car. Michelle can complete the work in 6 hours, while Nancy can complete the work in 3 hours. How many hours does the car washing take if they work together? 3 2 six eighths four thirds
we go right to the answer (otherwise it take like forever) but remember this simple trick \[\frac{6\times 3}{6+3}\]
got that ?
so 18/9 = 2
yes
Bob and Susie wash cars for extra money over the summer. Bob's income is determined by f(x) = 6x + 13, where x is the number of hours. Susie's income is g(x) = 4x + 18. If Bob and Susie were to combine their efforts, their income would be h(x) = f(x) + g(x). Assume Bob works 3 hours. Create the function h(x) and indicate if Bob will make more money working alone or by teaming with Susie. h(x) = 2x + 5, work alone h(x) = 2x + 5, team with Susie h(x) = 10x + 31, team with Susie h(x) = 10x + 31, work alone
see the trick? it is easy
yup
\[g(x) = 4x + 18\] \[h(x)=6x+13\] \[g(x)+h(x)=4x+18+6x+13\]
combine like terms,what do you get?
10x + 31
ok good so C or D
yup but i think its with team work so C?
not sure if bob works 3 hours alone he makes \[f(3)=6\times 3+13=18+13=31\]
oh so D
don't jump the gun
if they both work 3 hours they make a total of \pg(3)=10\times 3+31=61\]
oh
\[h(3)=10\times 3+31=61\]\]
if he has to split it, then yes he is better off working alone
so is its C then?
i think D not really clear, but i think D
ok
next?
What is the equation of the quadratic graph with a focus of (3, 6) and a directrix of y = 4?
this takes a second
k
half way between 6 and 4 is 5, so the vertex is \((3,5)\)
therefore it will look like \[4p(y-5)=(x-3)^2\] we need \(p\)
the distance between 4 and 5 is 1, so p = 1 and one answer is \[4(y-5)=(x-3)^2\] now sure what your answer choices look like
f(x) = one fourth (x − 3)2 + 1 f(x) = one fourth (x − 3)2 + 5 f(x) = −one fourth (x − 2)2 + 5 f(x) = −one fourth (x − 2)2
\[4(y-5)=(x-3)^2\\ y-5=\frac{1}{4}(x-3)^2\\ y=\frac{1}{4}(x-3)^2+5\]
thnx Which of the following is a solution of x2 + 2x + 8? 4 + i times the square root of 7 −1 + i times the square root of 7 2 + i times the square root of 7 −4 + i times the square root of 7
x^2 + 2x +8
you want do step by step? or wolfram it?
step by step so i can learn
ok a) subtract 8 from both sides, what do you get?
if that is not clear say so i will tell you
oh note that you are starting with \[x^2+2x+8=0\]
x^2 + 2x = 8
i meaN -8
ok good
SO X^2 + 2X = -8
\[x^2+2x=8\] now what is half of 2?`
oops \[x^2+2x=-8\] what is half of two?
1
so x^2 + x = -8/2?
no slow
oh sorry
half of 2 is 1, so we go right to \[(x+1)^2=-8+1^2\] or \[(x+1)^2=-7\]
ok
take the square root, get \[x+1=\pm\sqrt{-7}\] or \[x+1=\pm\sqrt{7}i\]
subtract 1, get \[x=-1\pm\sqrt{7}i\]
thnx
What are the possible numbers of positive, negative, and complex zeros of f(x) = -3x4 - 5x3 - x2 - 8x + 4? Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0 Positive: 1; negative: 3 or 1; complex: 2 or 0 Positive: 3 or 1; negative: 1; complex: 2 or 0 Positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
ok we do this, then i gotta split
\[f f(x) = -3x^4 - 5x^3 - x^2 - 8x + 4\]
it is a polynomial of degree 4, so it has 4 zeros for sure
there is one change in sign of the coefficients, which is a fancy way of saying that the go "minus, minus, minus, minus , PLUS" only once change in sign therefore there is one positive zero there cannot be no positive zeros because you count down by twos
\[f(x) = -3x^4 - 5x^3 - x^2 - 8x + 4\] \[f(-x) = -3x^4 + 5x^3 - x^2 + 8x + 4\]
here there are 3 changes in sign from -3 to +5, from +5 to -1 and from -1 tp +8 so there are either 3 negative zeros, or one negative zero
possibilities therefore are 1 positive, 3 negative (total of 4) or 1 positive, 1 negative 2 complex (total of 4)
now i really have to bolt ask your sister how to do the rest good luck!
thnx and ok bye
bye !

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