Question

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

Answer 1

Assuming `x!=0 and y!=0 and x!=y`

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

`color(white)("xxxxxxxx")`extract common factors

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

`color(white)("xxxxxxxx")` divide out common factors, factor numerator, & negate denominator

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

`color(white)("xxxxxxxx")`divide out common factor

`= -(x+y)`