Question

How do you simplify `x^3/ (x^2-y^2) + y^3/( y^2-x^2)`?

Answer 1

`(x^2+xy+y^2)/(x+y)`

Explanation:

`x^2/(x^2-y^2)+y^3/(y^2-x^2)`

`color(white)("XXX")=(x^3-y^3)/(x^2-y^2)`

`color(white)("XXX")=((x-y)(x^2+xy+y^2))/((x-y)(x+y)`

`color(white)("XXX")=(x^2+xy+y^2)/(x+y)`