Solve (x/y-y/x)divx-y/x

$$( \frac { x } { y } - \frac { y } { x } ) \div \frac { x - y } { x }$$

Evaluate

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

Short Solution Steps

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}.

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

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

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

Do the multiplications in xx-yy.

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-y in both numerator and denominator.

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

Expand

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

Short Solution Steps

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}.

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

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

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

Do the multiplications in xx-yy.

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-y in both numerator and denominator.

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