Solve 1/x^2-xy-1/y^2-xy/frac{1{x^2y-y^2x}}=

$$\frac { \frac { 1 } { x ^ { 2 } - x y } - \frac { 1 } { y ^ { 2 } - x y } } { \frac { 1 } { x ^ { 2 } y - y ^ { 2 } x } } =$$

Evaluate

$$x+y$$

Short Solution Steps

Factor x^{2}-xy. Factor y^{2}-xy.

$$\frac{\frac{1}{x\left(x-y\right)}-\frac{1}{y\left(-x+y\right)}}{\frac{1}{x^{2}y-y^{2}x}}$$

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

$$\frac{\frac{-y}{xy\left(-x+y\right)}-\frac{x}{xy\left(-x+y\right)}}{\frac{1}{x^{2}y-y^{2}x}}$$

Since \frac{-y}{xy\left(-x+y\right)} and \frac{x}{xy\left(-x+y\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-y-x}{xy\left(-x+y\right)}}{\frac{1}{x^{2}y-y^{2}x}}$$

Divide \frac{-y-x}{xy\left(-x+y\right)} by \frac{1}{x^{2}y-y^{2}x} by multiplying \frac{-y-x}{xy\left(-x+y\right)} by the reciprocal of \frac{1}{x^{2}y-y^{2}x}.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in x-y.

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

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

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

Expand the expression.

$$x+y$$

Expand

$$x+y$$

Short Solution Steps

Factor x^{2}-xy. Factor y^{2}-xy.

$$\frac{\frac{1}{x\left(x-y\right)}-\frac{1}{y\left(-x+y\right)}}{\frac{1}{x^{2}y-y^{2}x}}$$

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

$$\frac{\frac{-y}{xy\left(-x+y\right)}-\frac{x}{xy\left(-x+y\right)}}{\frac{1}{x^{2}y-y^{2}x}}$$

Since \frac{-y}{xy\left(-x+y\right)} and \frac{x}{xy\left(-x+y\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-y-x}{xy\left(-x+y\right)}}{\frac{1}{x^{2}y-y^{2}x}}$$

Divide \frac{-y-x}{xy\left(-x+y\right)} by \frac{1}{x^{2}y-y^{2}x} by multiplying \frac{-y-x}{xy\left(-x+y\right)} by the reciprocal of \frac{1}{x^{2}y-y^{2}x}.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in x-y.

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

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

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

Expand the expression.

$$x+y$$