1-x²/(x-2)² divide by (x-1)²/4-x²

Question

It's about algebraic expression III ..... Help me.. I don't know how to do.. Thanks.

Answer 1

(1-x²)/(x-2)²=(1-x)(1+x)/(x-2)²;

(x-1)²/(4-x²)=(x-1)²/[(2-x)(2+x)].

Note that (x-1)²=(1-x)² and (x-2)²=(2-x)²

Division is converted to multiplication by inverting the divisor:

(1-x)(1+x)/(2-x)²(2-x)(2+x)/(1-x)²=

(1+x)(2+x)/[(2-x)(1-x)].