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

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

Evaluate

$$\frac{x+2}{x-2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x+4}{x+4}.

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

Since \frac{x\left(x+4\right)}{x+4} and \frac{4}{x+4} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x\left(x+4\right)+4.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x+4}{x+4}.

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

Since \frac{x\left(x+4\right)}{x+4} and \frac{4x+4}{x+4} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x\left(x+4\right)-\left(4x+4\right).

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

Combine like terms in x^{2}+4x-4x-4.

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

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

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

Cancel out x+4 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

$$\frac{x+2}{x-2}$$

Expand

$$\frac{x+2}{x-2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x+4}{x+4}.

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

Since \frac{x\left(x+4\right)}{x+4} and \frac{4}{x+4} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x\left(x+4\right)+4.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x+4}{x+4}.

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

Since \frac{x\left(x+4\right)}{x+4} and \frac{4x+4}{x+4} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x\left(x+4\right)-\left(4x+4\right).

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

Combine like terms in x^{2}+4x-4x-4.

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

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

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

Cancel out x+4 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

$$\frac{x+2}{x-2}$$