先化简,再求值:(x^2-y^2/xy)÷(x+y)乘(x/x-y)^3,其中x=-1/2,y=-1

题目

先化简,再求值:(x^2-y^2/xy)÷(x+y)乘(x/x-y)^3,其中x=-1/2,y=-1

答案

[(x²-y²)/(xy)]÷(x+y)×[x/(x-y)]³
=[(x-y)/(xy)]×x³/(x-y)³
=x²/[y×(x-y)²]
=(1/4)/{-1×[(-1/2)-(-1)]²}
=-1