x-y/x^2-2xy+y^2-xy+y^2/x^2-y^2先化简再求值,其中（x-2）^2+|y-3|=0
问题描述：
x-y/x^2-2xy+y^2-xy+y^2/x^2-y^2先化简再求值,其中（x-2）^2+|y-3|=0
答
已知（x-2）^2+|y-3|=0，那么要使上式成立，须使得：
x-2=0且y-3=0
即得x=2，y=3
所以：
(x-y)/(x²-2xy+y²)- (xy+y²)/(x²-y²)
=(x-y)/(x-y)² - y(x+y)/[(x-y)(x+y)]
=1/(x-y) - y/(x-y)
=(1-y)/(x-y)
=(1-3)/(2-3)
=-2/(-1)
=2
答
(x-y)/(x^2-2xy+y^2)-(xy+y^2)/(x^2-y^2)
=(x-y)/(x-y)²-y(x+y)/(x+y)(x-y)
=1/(x-y)-y/(x-y)
=(1-y)/(x-y)
∵(x-2)²+|y-3|=0
∴(x-2)²=0 |y-3|=0
即x=2 y=3
∴原式=(1-3)/(2-3)=2