## heathernelly Group Title 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 one year ago one year ago

1. heathernelly Group Title

2. phi Group Title

can you factor the quadratic ?

3. heathernelly Group Title

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

4. phi Group Title

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

5. heathernelly Group Title

hm, I'm not sure..

6. phi Group Title

look for a common factor (hint: z)

7. heathernelly Group Title

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

8. phi Group Title

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

9. heathernelly Group Title

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

10. heathernelly Group Title

oh, so i got it right? :D

11. phi Group Title

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

12. phi Group Title

so what do we have so far?

13. heathernelly Group Title

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

14. phi Group Title

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

15. heathernelly Group Title

just what we wrote up there? :/

16. phi Group Title

like this $\frac{z\cdot z}{(z+1)} \cdot \frac{(z+2)(z+1) }{z(z+3)}$

17. heathernelly Group Title

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

18. phi Group Title

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

19. heathernelly Group Title

restriction is that x cannot be 0 or -3?

20. phi Group Title

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

21. heathernelly Group Title

oh

22. heathernelly Group Title

-1?

23. phi Group Title

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

24. phi Group Title

no -1. You almost have it. $\frac{z\cdot z \cdot (z+2)(z+1) }{z(z+3)(z+1)}$

25. phi Group Title

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

26. heathernelly Group Title

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

27. phi Group Title

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

28. heathernelly Group Title

you are awesome! tytyty :D x

29. phi Group Title

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

30. phi Group Title