Question

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

Answer 1

`(x^2-y^2)/(xy+x^2) div (y-x)/(x+y)= -(x+y)/x`

Explanation:

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

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

`color(white)("XXXX")` `=((x+y)(x-y))/(x(x+y))*(x+y)/((-1)(x-y))`

`color(white)("XXXX")` `=(cancel((x+y))cancel((x-y)))/(xcancel((x+y)))*(x+y)/((-1)cancel((x-y)))`

`color(white)("XXXX")` `= -(x+y)/x`