Solve frac{x^{2}-4y^{2}}{2x^2-5xy+2y^2}*x^2-xy/x+ydivx^2-xy/2x-y

$$\frac { x ^ { 2 } - 4 y ^ { 2 } } { 2 x ^ { 2 } - 5 x y + 2 y ^ { 2 } } \times \frac { x ^ { 2 } - x y } { x + y } \div \frac { x ^ { 2 } - x y } { 2 x - y }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-4y^{2}}{2x^{2}-5xy+2y^{2}}.

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

Cancel out x-2y in both numerator and denominator.

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

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

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

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

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

Cancel out \left(2x-y\right)\left(x^{2}-xy\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-4y^{2}}{2x^{2}-5xy+2y^{2}}.

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

Cancel out x-2y in both numerator and denominator.

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

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

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

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

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

Cancel out \left(2x-y\right)\left(x^{2}-xy\right) in both numerator and denominator.

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