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How do you simplify $\frac{x^{3} y - x y^{3}}{x y^{2} - x^{2} y}$ $(x^3y - xy^3)/(xy^2 - x^2 y)$ ?

1 Answer

May 29, 2015

Assuming $x \neq 0 and y \neq 0 and x \neq y$ $x!=0 and y!=0 and x!=y$

$\frac{x^{3} y - x y^{3}}{x y^{2} - x^{2} y}$ $(x^3y - xy^3)/(xy^2-x^2y)$

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

$= \frac{(x y) (x^{2} - y^{2})}{(x y) (y - x)}$ $=((xy)(x^2-y^2))/((xy)(y-x))$

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

$= \frac{(x + y) (x - y)}{(- 1) (x - y)}$ $= ((x+y)(x-y))/((-1)(x-y))$

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

$= - (x + y)$ $= -(x+y)$

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