Solve (2/x-5/y)div4/xy

$$( \frac { 2 } { x } - \frac { 5 } { y } ) \div \frac { 4 } { x y }$$

Evaluate

$$\frac{y}{2}-\frac{5x}{4}$$

Short Solution Steps

Divide \frac{2}{x}-\frac{5}{y} by \frac{4}{xy} by multiplying \frac{2}{x}-\frac{5}{y} by the reciprocal of \frac{4}{xy}.

$$\frac{\left(\frac{2}{x}-\frac{5}{y}\right)xy}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and y is xy. Multiply \frac{2}{x} times \frac{y}{y}. Multiply \frac{5}{y} times \frac{x}{x}.

$$\frac{\left(\frac{2y}{xy}-\frac{5x}{xy}\right)xy}{4}$$

Since \frac{2y}{xy} and \frac{5x}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2y-5x}{xy}xy}{4}$$

Express \frac{2y-5x}{xy}x as a single fraction.

$$\frac{\frac{\left(2y-5x\right)x}{xy}y}{4}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{-5x+2y}{y}y}{4}$$

Cancel out y and y.

$$\frac{-5x+2y}{4}$$

Expand

$$\frac{y}{2}-\frac{5x}{4}$$

Short Solution Steps

Divide \frac{2}{x}-\frac{5}{y} by \frac{4}{xy} by multiplying \frac{2}{x}-\frac{5}{y} by the reciprocal of \frac{4}{xy}.

$$\frac{\left(\frac{2}{x}-\frac{5}{y}\right)xy}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and y is xy. Multiply \frac{2}{x} times \frac{y}{y}. Multiply \frac{5}{y} times \frac{x}{x}.

$$\frac{\left(\frac{2y}{xy}-\frac{5x}{xy}\right)xy}{4}$$

Since \frac{2y}{xy} and \frac{5x}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2y-5x}{xy}xy}{4}$$

Express \frac{2y-5x}{xy}x as a single fraction.

$$\frac{\frac{\left(2y-5x\right)x}{xy}y}{4}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{-5x+2y}{y}y}{4}$$

Cancel out y and y.

$$\frac{-5x+2y}{4}$$