I don't understand this (x-y)/(x+y) + (x+y)/(x-y)

Answer 1

Just as with normal fractions, you need to find a common denominator.

For example, with

2/3 + 3/5, the commond denominator is (3)(5)

Here, you will have a common denominator of (x+y)(x-y)

So, you will wind up with

(x-y)(x-y)/(x+y)(x-y) + (x+y)(x+y)/(x-y)(x+y)

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