Solve xdiv(1/x-1/y)

$$x \div ( \frac { 1 } { x } - \frac { 1 } { y } )$$

Evaluate

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

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}.

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

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

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

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

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

Multiply x and x to get x^{2}.

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

Differentiate w.r.t. x

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