x^2-y^2/x^2+2xy+y^2-x+y/x-y,其中x=1,y=-3

题目

x^2-y^2/x^2+2xy+y^2-x+y/x-y,其中x=1,y=-3
带数求值!^-^
下列运算正确的是 （ ）
A.a/a-b-b/b-a=1 B.m/a-n/b=m-n/a-b
C.b/a-b+1/a=1/a D.2/a-b-a+b/a^2-b^2=1/a-b

答案

x^2-y^2/x^2+2xy+y^2-x+y/x-y=(x+y)(x-y)/(x+y)²-(x+y)/(x-y)=(x-y)/(x+y)-(x+y)/(x-y)=-4xy/(x²-y²)当x=1,y=-3时原式=12/(1-9)=-3/2D.2/a-b-a+b/a^2-b^2=1/a-b