先化简,再求值:(2-x/x^2+x)/(x^2-3x/x^2+2x+1)x(9-x^2/4-2x),其中x=-2

问题描述:

先化简,再求值:(2-x/x^2+x)/(x^2-3x/x^2+2x+1)x(9-x^2/4-2x),其中x=-2

:(2-x/x^2+x)/(x^2-3x/x^2+2x+1)x(9-x^2/4-2x),
=[-(x-2)]/x(x+1)×(x+1)²/x(x-3)×[-(x+3)(x-3)]/[-2(x-2)]
=-1/x×(x+1)/x×(x+3)/2
=-(x+1)(x+3)/2x²