Solve frac{2x^{3}+2x^{2}y}{x^{2}y-xy^2}*xy^2-y^3/x^2+xy

$$\frac { 2 x ^ { 3 } + 2 x ^ { 2 } y } { x ^ { 2 } y - x y ^ { 2 } } \cdot \frac { x y ^ { 2 } - y ^ { 3 } } { x ^ { 2 } + x y }$$

Evaluate

$$2y$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{3}+2x^{2}y}{x^{2}y-xy^{2}}.

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

Cancel out x in both numerator and denominator.

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

Multiply \frac{2x\left(x+y\right)}{y\left(x-y\right)} times \frac{xy^{2}-y^{3}}{x^{2}+xy} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

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

$$2y$$

Expand

$$2y$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{3}+2x^{2}y}{x^{2}y-xy^{2}}.

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

Cancel out x in both numerator and denominator.

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

Multiply \frac{2x\left(x+y\right)}{y\left(x-y\right)} times \frac{xy^{2}-y^{3}}{x^{2}+xy} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

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

$$2y$$