Solve 1/x+1/y/frac{x{y}-y/x}=

$$\frac { \frac { 1 } { x } + \frac { 1 } { y } } { \frac { x } { y } - \frac { y } { x } } =$$

Evaluate

$$-\frac{1}{y-x}$$

Short Solution Steps

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

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

Since \frac{y}{xy} and \frac{x}{xy} have the same denominator, add them by adding their numerators.

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

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

$$\frac{\frac{y+x}{xy}}{\frac{xx}{xy}-\frac{yy}{xy}}$$

Since \frac{xx}{xy} and \frac{yy}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{y+x}{xy}}{\frac{xx-yy}{xy}}$$

Do the multiplications in xx-yy.

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

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

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

Cancel out xy in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+y in both numerator and denominator.

$$\frac{1}{x-y}$$

Expand

$$\frac{1}{x-y}$$

Short Solution Steps

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

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

Since \frac{y}{xy} and \frac{x}{xy} have the same denominator, add them by adding their numerators.

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

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

$$\frac{\frac{y+x}{xy}}{\frac{xx}{xy}-\frac{yy}{xy}}$$

Since \frac{xx}{xy} and \frac{yy}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{y+x}{xy}}{\frac{xx-yy}{xy}}$$

Do the multiplications in xx-yy.

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

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

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

Cancel out xy in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+y in both numerator and denominator.

$$\frac{1}{x-y}$$