Question

先化简再求值:（x+y/x-y-x-y/x+y）*(1/x^2-1/y^2)其中x=1/4，y=4

Answer 1

原式=(x+y)²-(x-y)²/(x+y)(x-y)*(y²-x²)/x²y²
=4xy/x²-y²*y²-x²/x²y²
=-4/xy
把x=1/4，y=4代入上式
得：-4/（1/4*4）=-4

Answer 2

(x+y/x-y-x-y/x+y)×(1/x²-1/y²)
=[(x-x)+(y/x-y/x)+(y-y)]×(1/x²-1/y²)
=0×(1/x²-1/y²)
=0