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

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

Evaluate

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

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

$$\frac{x-4}{\frac{xx}{4x}-\frac{4\times 4}{4x}}$$

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

$$\frac{x-4}{\frac{xx-4\times 4}{4x}}$$

Do the multiplications in xx-4\times 4.

$$\frac{x-4}{\frac{x^{2}-16}{4x}}$$

Divide x-4 by \frac{x^{2}-16}{4x} by multiplying x-4 by the reciprocal of \frac{x^{2}-16}{4x}.

$$\frac{\left(x-4\right)\times 4x}{x^{2}-16}$$

Factor the expressions that are not already factored.

$$\frac{4x\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}$$

Cancel out x-4 in both numerator and denominator.

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

Expand

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

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

$$\frac{x-4}{\frac{xx}{4x}-\frac{4\times 4}{4x}}$$

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

$$\frac{x-4}{\frac{xx-4\times 4}{4x}}$$

Do the multiplications in xx-4\times 4.

$$\frac{x-4}{\frac{x^{2}-16}{4x}}$$

Divide x-4 by \frac{x^{2}-16}{4x} by multiplying x-4 by the reciprocal of \frac{x^{2}-16}{4x}.

$$\frac{\left(x-4\right)\times 4x}{x^{2}-16}$$

Factor the expressions that are not already factored.

$$\frac{4x\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}$$

Cancel out x-4 in both numerator and denominator.

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