heathernelly
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



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heathernelly
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phi
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can you factor the quadratic ?

heathernelly
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can you factor all of it? :S is it (z+2)(z+1)?

phi
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you can check: multiply (z+2)(z+1) = z^2 +2z + z +2 = x^2 +3z+2
yes that works.
how about the bottom ?

heathernelly
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hm, I'm not sure..

phi
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look for a common factor (hint: z)

heathernelly
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i don't know how to factor the bottom half, i'm really bad at factoring

phi
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example: x(x+2) = x^2 +2x
or undoing it x^2 +2x =x(x+2)

heathernelly
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x(x+3)? i really don't know :/

heathernelly
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oh, so i got it right? :D

phi
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yes, except they are using z
z(z+3) can be written as z^2 +3z (distribute the z)
so yes

phi
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so what do we have so far?

heathernelly
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well that's easy :) what's next?

phi
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write down what we have after all the factoring , and see what we have

heathernelly
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just what we wrote up there? :/

phi
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like this
\[ \frac{z\cdot z}{(z+1)} \cdot \frac{(z+2)(z+1) }{z(z+3)} \]

heathernelly
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then cross out z+1 and z...which would be z+2 / z+3?

phi
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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

heathernelly
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restriction is that x cannot be 0 or 3?

phi
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yes, but I think there is another z up top. Check your canceling.

heathernelly
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oh

heathernelly
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1?

phi
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yes, up top we had z^2 or z*z and only 1 z in the bottom

phi
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no 1. You almost have it.
\[ \frac{z\cdot z \cdot (z+2)(z+1) }{z(z+3)(z+1)} \]

phi
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and yes, the restricted values are 0, 3, and 1
what do you have for the final answer?

heathernelly
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hm, z^2+2z/z+3? :S

phi
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yes, with restrictions that z is not 0, 1 or 3

heathernelly
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you are awesome! tytyty :D x

phi
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though I would put parens around it just to be clear.
(z^2+2z)/(z+3)
and no :S (ha ha)


heathernelly
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haha, you mean yes! thanks :)

heathernelly
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i'll check them out! :D