Question

分式运算

x-y/(x+y)(x-y)+y-x/(y+x)(y-x) 请写下具体步骤 谢谢！
请用两种方法 谢谢！ 答案上写的结果是2/x+y 但我不知道步骤

Answer 1

方法一：直接约分，特别简单
原式=1/(x+y)+1/(x+y)=2/x+y

方法二：先将分母变得一样
原式=x-y/(x+y)(x-y)+ x-y/(y+x)(x-y) (因为分子分母都加了-号，分子由y-x变x-y，分母中的后一个括号里的y-x变成x-y,现在两个分式的分母都相同了，然后相加)
=（x-y）+(x-y)/(x+y)(x-y)（分母不变，分子相加）
=2(x-y)/(x+y)(x-y)（然后上下约分）
=2/x+y

Answer 2

原式=x-y/(x+y)(x-y)+y+x/(x+y)(x-y)
=x+y-(y-x)/(x+y)(x-y)
=x+y+1/(x+y)

原式=x(x+y)(x-y)/(x+y)(x-y)-y/(x+y)(x-y)+y(x+y)(x-y)/(x+y)(x-y)+x/(x+y)(x-y)
=x+y+1/(x+y)

Answer 3

首先，（x-y）/(x+y)(x-y)中x-y是可以约掉的
（y-x）/(y+x)(y-x)中y-x也是可以约掉的，
所以只剩1/（x+y）+1/（x+y）
所以是2/x+y

Answer 4

1235

Answer 5

原式=x+y-[x+y/(x+y)(x-y)]
再通分