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

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

Evaluate

$$\frac{x\left(x+y\right)}{y}$$

Short Solution Steps

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

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

Cancel out x+y in both numerator and denominator.

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

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

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

Cancel out x-y in both numerator and denominator.

$$\frac{x\left(x+y\right)}{x-y}\times \frac{x-y}{y}$$

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

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

Cancel out x-y in both numerator and denominator.

$$\frac{x\left(x+y\right)}{y}$$

Use the distributive property to multiply x by x+y.

$$\frac{x^{2}+xy}{y}$$

Expand

$$\frac{x^{2}}{y}+x$$

Short Solution Steps

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

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

Cancel out x+y in both numerator and denominator.

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

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

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

Cancel out x-y in both numerator and denominator.

$$\frac{x\left(x+y\right)}{x-y}\times \frac{x-y}{y}$$

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

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

Cancel out x-y in both numerator and denominator.

$$\frac{x\left(x+y\right)}{y}$$

Use the distributive property to multiply x by x+y.

$$\frac{x^{2}+xy}{y}$$