Solve x^3y-xy^3/(x-y)(x+y):xy+x/y^2+y

$$\frac { x ^ { 3 } y - x y ^ { 3 } } { ( x - y ) ( x + y ) } : \frac { x y + x } { y ^ { 2 } + y }$$

Evaluate

$$y^{2}$$

Short Solution Steps

Divide \frac{x^{3}y-xy^{3}}{\left(x-y\right)\left(x+y\right)} by \frac{xy+x}{y^{2}+y} by multiplying \frac{x^{3}y-xy^{3}}{\left(x-y\right)\left(x+y\right)} by the reciprocal of \frac{xy+x}{y^{2}+y}.

$$\frac{\left(x^{3}y-xy^{3}\right)\left(y^{2}+y\right)}{\left(x-y\right)\left(x+y\right)\left(xy+x\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(y+1\right)\left(x+y\right)\left(x-y\right)y^{2}}{x\left(y+1\right)\left(x+y\right)\left(x-y\right)}$$

Cancel out x\left(y+1\right)\left(x+y\right)\left(x-y\right) in both numerator and denominator.

$$y^{2}$$

Expand

$$y^{2}$$

Short Solution Steps

Divide \frac{x^{3}y-xy^{3}}{\left(x-y\right)\left(x+y\right)} by \frac{xy+x}{y^{2}+y} by multiplying \frac{x^{3}y-xy^{3}}{\left(x-y\right)\left(x+y\right)} by the reciprocal of \frac{xy+x}{y^{2}+y}.

$$\frac{\left(x^{3}y-xy^{3}\right)\left(y^{2}+y\right)}{\left(x-y\right)\left(x+y\right)\left(xy+x\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(y+1\right)\left(x+y\right)\left(x-y\right)y^{2}}{x\left(y+1\right)\left(x+y\right)\left(x-y\right)}$$

Cancel out x\left(y+1\right)\left(x+y\right)\left(x-y\right) in both numerator and denominator.

$$y^{2}$$