Expert: Scott A Wilson - 7/26/2010

Question
PART 6

1) Simplify.
(z^3-4z)/(z^2-4z+4)

a)z
b)z/4
c)z(z+2)/z-2
d)z^2+2z/2


2)(a-x)^2/x^2-a^2

a)1
b)x-a/x+a
c)x-a
d)-a-x/x+a

3) Simplify: (9-4z^2)/(6z^2-5z-6)

a)-1
b)-3-2z/3z+2
c)3+2z
d)3z-2

Answer
1) Factor out a z on the top.
Note that what is left on top is the difference of squares and the bottom is the square of (z-2).
This means the problem is [z(z-2)(z+2)]/[(z-2)(z-2)], and a z-2 can be cancelled in the top and bottom.

2) This is the same as (a-x)²/[(x-a)(x+a)]; then note that (a-x)/(x-a) = -1;
this gives (x-2)/(x+a).

3) The top is (3-2z)(3+2z); the bottom is (3z+2)(2z-3); note that (3-2z)/(2z-3) = -1.
This leaves -(3+2z)/(3z+2).