Question

数学，大家帮帮我

（1）x的-2次方-y的-2次方分之（x的-1次方+y的-1次方）的2次方
（2）（xy的-1次方-x的-1次方y）÷（x的-1次方+y的-1次方）
（3）（x的2次方-2x+1分之x+1）的-1次方×（x+1分之x-1）的-2次方
计算题【要过程】
结果写成只含有正整数幂的形式

Answer 1

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

=(x/y-y/x)/(1/x+1/y)
=[(x^2-y^2)/(xy)]/[(x+y)/(xy)]
=x-y
(3) [ (x+1)/(x^2-2x+1)]^(-1)×[(x-1)/(x+1)]^(-2)
=(x-1)^2/(x+1)×[(x+1)^2/(x-1)^2]
=x+1