Solve 1/y-1/x/frac{x{y}-4/x}

$$\frac { \frac { 1 } { y } - \frac { 1 } { x } } { \frac { x } { y } - \frac { 4 } { x } }$$

Evaluate

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

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{1}{y} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{y}{y}.

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

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

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

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{4}{x} times \frac{y}{y}.

$$\frac{\frac{x-y}{xy}}{\frac{xx}{xy}-\frac{4y}{xy}}$$

Since \frac{xx}{xy} and \frac{4y}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-y}{xy}}{\frac{xx-4y}{xy}}$$

Do the multiplications in xx-4y.

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

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

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

Cancel out xy in both numerator and denominator.

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

Expand

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

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{1}{y} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{y}{y}.

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

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

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

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{4}{x} times \frac{y}{y}.

$$\frac{\frac{x-y}{xy}}{\frac{xx}{xy}-\frac{4y}{xy}}$$

Since \frac{xx}{xy} and \frac{4y}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-y}{xy}}{\frac{xx-4y}{xy}}$$

Do the multiplications in xx-4y.

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

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

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

Cancel out xy in both numerator and denominator.

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