Simplify the following...?

Question

Simplify the following and state the restrictions on the variables.

x^2+3x+2/x^2-4 X x^2-2x+1/1-x^2

I got
(x+2)(x+1)/(x+2)(x-2) X (x-1)(x-1)/(1-x)(1+x)

I know you're suppose to cancel out (x+2), however does (x-1) cancel out (1-x)? Are they the same? I can't seem to figure that out. Thanks for any help.

Answer 1

If you have this:

(x - 1) /( 1- x)

You could cancel it with a little manipulation.

(x - 1) / ( -(-1 + x))

(x - 1) / (- (x - 1))

-1

So, factor out a negative 1 and you cancel the (1 - x) and (x - 1).

However, (1 + x) = (x + 1) so those could cancel.

This is what I got.

- ( (x - 1) / (x + 2) )

Answer 2

(x-1) = -(1-x)