anonymous
  • anonymous
PLEASE HELP!!! What is the product in simplest form? State any restrictions on the variable. z^2/z+1 times z^2+3z+2/z^2+3z
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
phi
  • phi
can you factor the quadratic ?
anonymous
  • anonymous
can you factor all of it? :S is it (z+2)(z+1)?

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phi
  • phi
you can check: multiply (z+2)(z+1) = z^2 +2z + z +2 = x^2 +3z+2 yes that works. how about the bottom ?
anonymous
  • anonymous
hm, I'm not sure..
phi
  • phi
look for a common factor (hint: z)
anonymous
  • anonymous
i don't know how to factor the bottom half, i'm really bad at factoring
phi
  • phi
example: x(x+2) = x^2 +2x or undoing it x^2 +2x =x(x+2)
anonymous
  • anonymous
x(x+3)? i really don't know :/
anonymous
  • anonymous
oh, so i got it right? :D
phi
  • phi
yes, except they are using z z(z+3) can be written as z^2 +3z (distribute the z) so yes
phi
  • phi
so what do we have so far?
anonymous
  • anonymous
well that's easy :) what's next?
phi
  • phi
write down what we have after all the factoring , and see what we have
anonymous
  • anonymous
just what we wrote up there? :/
phi
  • phi
like this \[ \frac{z\cdot z}{(z+1)} \cdot \frac{(z+2)(z+1) }{z(z+3)} \]
anonymous
  • anonymous
then cross out z+1 and z...which would be z+2 / z+3?
phi
  • phi
now you (hopefully) know that when you divide something by itself you get 1, so we an cancel terms that are in both the top and bottom
anonymous
  • anonymous
restriction is that x cannot be 0 or -3?
phi
  • phi
yes, but I think there is another z up top. Check your canceling.
anonymous
  • anonymous
oh
anonymous
  • anonymous
-1?
phi
  • phi
yes, up top we had z^2 or z*z and only 1 z in the bottom
phi
  • phi
no -1. You almost have it. \[ \frac{z\cdot z \cdot (z+2)(z+1) }{z(z+3)(z+1)} \]
phi
  • phi
and yes, the restricted values are 0, -3, and -1 what do you have for the final answer?
anonymous
  • anonymous
hm, z^2+2z/z+3? :S
phi
  • phi
yes, with restrictions that z is not 0, -1 or -3
anonymous
  • anonymous
you are awesome! tytyty :D x
phi
  • phi
though I would put parens around it just to be clear. (z^2+2z)/(z+3) and no :S (ha ha)
phi
  • phi
Here are some videos http://www.khanacademy.org/math/algebra/rational-expressions/simplifying-rational-alg/v/simplifying-rational-expressions-introduction they are very helpful
anonymous
  • anonymous
haha, you mean yes! thanks :)
anonymous
  • anonymous
i'll check them out! :D

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