Question

先化简再求值 （1）已知分式x的2次方y-2xy的2次方分之x的3次方-2x的2次方y,其中x=3,y=1

Answer 1

(1)(x^3-2x^2y)/(x^2-2xy^2)=〔x^2(x-2y)〕/〔xy(x-2y)〕=x/y=3

(2)(x^2+2xy+y^2)/(x^2-xy-2y^2)=(x+y)^2/〔(x-2y)(x+y)〕=(x+y)/(x-2y)

由x/y=1/2推出y=2x代入上式得(x+2x)/(x-4x)=-1