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

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

Evaluate

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

Short Solution Steps

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

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

Cancel out x+y in both numerator and denominator.

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

Multiply \frac{x+y}{x-y} times \frac{2x^{2}-xy-y^{2}}{x^{2}-xy-2y^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

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

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

Expand

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

Short Solution Steps

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

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

Cancel out x+y in both numerator and denominator.

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

Multiply \frac{x+y}{x-y} times \frac{2x^{2}-xy-y^{2}}{x^{2}-xy-2y^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

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

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