Solve x^2-5xy/x-y+y^2-5xy/y-x

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

Evaluate

$$x+y$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-y and y-x is -x+y. Multiply \frac{x^{2}-5xy}{x-y} times \frac{-1}{-1}.

$$\frac{-\left(x^{2}-5xy\right)}{-x+y}+\frac{y^{2}-5xy}{-x+y}$$

Since \frac{-\left(x^{2}-5xy\right)}{-x+y} and \frac{y^{2}-5xy}{-x+y} have the same denominator, add them by adding their numerators.

$$\frac{-\left(x^{2}-5xy\right)+y^{2}-5xy}{-x+y}$$

Do the multiplications in -\left(x^{2}-5xy\right)+y^{2}-5xy.

$$\frac{-x^{2}+5xy+y^{2}-5xy}{-x+y}$$

Combine like terms in -x^{2}+5xy+y^{2}-5xy.

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

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

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

Extract the negative sign in x-y.

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

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

$$-\left(-x-y\right)$$

Expand the expression.

$$x+y$$

Expand

$$x+y$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-y and y-x is -x+y. Multiply \frac{x^{2}-5xy}{x-y} times \frac{-1}{-1}.

$$\frac{-\left(x^{2}-5xy\right)}{-x+y}+\frac{y^{2}-5xy}{-x+y}$$

Since \frac{-\left(x^{2}-5xy\right)}{-x+y} and \frac{y^{2}-5xy}{-x+y} have the same denominator, add them by adding their numerators.

$$\frac{-\left(x^{2}-5xy\right)+y^{2}-5xy}{-x+y}$$

Do the multiplications in -\left(x^{2}-5xy\right)+y^{2}-5xy.

$$\frac{-x^{2}+5xy+y^{2}-5xy}{-x+y}$$

Combine like terms in -x^{2}+5xy+y^{2}-5xy.

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

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

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

Extract the negative sign in x-y.

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

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

$$-\left(-x-y\right)$$

Expand the expression.

$$x+y$$