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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
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  • phi
can you factor the quadratic ?
can you factor all of it? :S is it (z+2)(z+1)?

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Other answers:

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

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