先化简再求值 (x+2/x^2-2x - x-1/x^2-4x+4 )除4-x/x其中x=-3

题目

先化简再求值 (x+2/x^2-2x - x-1/x^2-4x+4 )除4-x/x其中x=-3
需大致过程.谢谢.

答案

[(x+2)/(x^2-2x)-(x-1)/(x^2-4x+4)]÷[(4-x)/x]
=[(x+2)/x(x-2)-(x-1)/(x-2)²]÷[(4-x)/x]
=[(x+2)(x-2)-x(x-1)]/x(x-2)²÷[(4-x)/x]
=[(x-4)/x(x-2)²] * [x/(4-x)]
=-1/(x-2)²
当x=-3时,原式=-1/(-3-2)²=-1/25