化简(1/(x-y)-1/(x+y))/(2y/(x^2-2xy+y^2))

(1/(x-y)-1/(x+y))/(2y/(x^2-2xy+y^2))
先对分子通分,公分母是(x-y)(x+y)
=([(x+y)-(x-y)]/[(x-y)(x+y)])÷[2y/(x-y)²]
=(2y/[(x-y)(x+y)])÷[2y/(x-y)²]
=(x-y)²/[(x-y)(x+y)]
约分,上下同时约去公因子(x-y)
=(x-y)/(x+y)

公式:x²-2xy+y²=(x+y)²

(1/(x-y)-1/(x+y))/(2y/(x^2-2xy+y^2))
＝(1/(x-y)-1/(x+y))/（2y/(x-y)^2)
=(2y/(x-y)(x+y))/（2y/(x-y)^2)
=(x-y)/(x+y)