Solve (x/y-y/x)*3x/x-y

$$( \frac { x } { y } - \frac { y } { x } ) \cdot \frac { 3 x } { x - y }$$

Evaluate

$$\frac{3\left(x+y\right)}{y}$$

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}.

$$\left(\frac{xx}{xy}-\frac{yy}{xy}\right)\times \frac{3x}{x-y}$$

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

$$\frac{xx-yy}{xy}\times \frac{3x}{x-y}$$

Do the multiplications in xx-yy.

$$\frac{x^{2}-y^{2}}{xy}\times \frac{3x}{x-y}$$

Multiply \frac{x^{2}-y^{2}}{xy} times \frac{3x}{x-y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-y^{2}\right)\times 3x}{xy\left(x-y\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{3\left(x^{2}-y^{2}\right)}{y\left(x-y\right)}$$

Factor the expressions that are not already factored.

$$\frac{3\left(x+y\right)\left(x-y\right)}{y\left(x-y\right)}$$

Cancel out x-y in both numerator and denominator.

$$\frac{3\left(x+y\right)}{y}$$

Expand the expression.

$$\frac{3x+3y}{y}$$

Expand

$$\frac{3\left(x+y\right)}{y}$$

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}.

$$\left(\frac{xx}{xy}-\frac{yy}{xy}\right)\times \frac{3x}{x-y}$$

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

$$\frac{xx-yy}{xy}\times \frac{3x}{x-y}$$

Do the multiplications in xx-yy.

$$\frac{x^{2}-y^{2}}{xy}\times \frac{3x}{x-y}$$

Multiply \frac{x^{2}-y^{2}}{xy} times \frac{3x}{x-y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-y^{2}\right)\times 3x}{xy\left(x-y\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{3\left(x^{2}-y^{2}\right)}{y\left(x-y\right)}$$

Factor the expressions that are not already factored.

$$\frac{3\left(x+y\right)\left(x-y\right)}{y\left(x-y\right)}$$

Cancel out x-y in both numerator and denominator.

$$\frac{3\left(x+y\right)}{y}$$

Expand the expression.

$$\frac{3x+3y}{y}$$