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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x is 4x. Multiply \frac{y}{4} times \frac{x}{x}. Multiply \frac{4}{x} times \frac{4}{4}.

$$\frac{\frac{yx}{4x}-\frac{4\times 4}{4x}}{-\frac{y}{x}}$$

Since \frac{yx}{4x} and \frac{4\times 4}{4x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{yx-4\times 4}{4x}}{-\frac{y}{x}}$$

Do the multiplications in yx-4\times 4.

$$\frac{\frac{yx-16}{4x}}{-\frac{y}{x}}$$

Express \frac{\frac{yx-16}{4x}}{-\frac{y}{x}} as a single fraction.

$$\frac{yx-16}{4x\left(-\frac{y}{x}\right)}$$

Express 4\left(-\frac{y}{x}\right) as a single fraction.

$$\frac{yx-16}{\frac{-4y}{x}x}$$

Cancel out x and x.

$$\frac{yx-16}{-4y}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x is 4x. Multiply \frac{y}{4} times \frac{x}{x}. Multiply \frac{4}{x} times \frac{4}{4}.

$$\frac{\frac{yx}{4x}-\frac{4\times 4}{4x}}{-\frac{y}{x}}$$

Since \frac{yx}{4x} and \frac{4\times 4}{4x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{yx-4\times 4}{4x}}{-\frac{y}{x}}$$

Do the multiplications in yx-4\times 4.

$$\frac{\frac{yx-16}{4x}}{-\frac{y}{x}}$$

Express \frac{\frac{yx-16}{4x}}{-\frac{y}{x}} as a single fraction.

$$\frac{yx-16}{4x\left(-\frac{y}{x}\right)}$$

Express 4\left(-\frac{y}{x}\right) as a single fraction.

$$\frac{yx-16}{\frac{-4y}{x}x}$$

Cancel out x and x.

$$\frac{yx-16}{-4y}$$