Solve x+2x/x-2/1+frac{4{(x+2)(x-2)}}

$$\frac { x + \frac { 2 x } { x - 2 } } { 1 + \frac { 4 } { ( x + 2 ) ( x - 2 ) } }$$

Evaluate

$$x+2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x-2}{x-2}.

$$\frac{\frac{x\left(x-2\right)}{x-2}+\frac{2x}{x-2}}{1+\frac{4}{\left(x+2\right)\left(x-2\right)}}$$

Since \frac{x\left(x-2\right)}{x-2} and \frac{2x}{x-2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x\left(x-2\right)+2x}{x-2}}{1+\frac{4}{\left(x+2\right)\left(x-2\right)}}$$

Do the multiplications in x\left(x-2\right)+2x.

$$\frac{\frac{x^{2}-2x+2x}{x-2}}{1+\frac{4}{\left(x+2\right)\left(x-2\right)}}$$

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

$$\frac{\frac{x^{2}}{x-2}}{1+\frac{4}{\left(x+2\right)\left(x-2\right)}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(x+2\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}.

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

Since \frac{\left(x+2\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)} and \frac{4}{\left(x+2\right)\left(x-2\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x+2\right)\left(x-2\right)+4.

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

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

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

Divide \frac{x^{2}}{x-2} by \frac{x^{2}}{\left(x+2\right)\left(x-2\right)} by multiplying \frac{x^{2}}{x-2} by the reciprocal of \frac{x^{2}}{\left(x+2\right)\left(x-2\right)}.

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

Cancel out \left(x-2\right)x^{2} in both numerator and denominator.

$$x+2$$

Expand

$$x+2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x-2}{x-2}.

$$\frac{\frac{x\left(x-2\right)}{x-2}+\frac{2x}{x-2}}{1+\frac{4}{\left(x+2\right)\left(x-2\right)}}$$

Since \frac{x\left(x-2\right)}{x-2} and \frac{2x}{x-2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x\left(x-2\right)+2x}{x-2}}{1+\frac{4}{\left(x+2\right)\left(x-2\right)}}$$

Do the multiplications in x\left(x-2\right)+2x.

$$\frac{\frac{x^{2}-2x+2x}{x-2}}{1+\frac{4}{\left(x+2\right)\left(x-2\right)}}$$

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

$$\frac{\frac{x^{2}}{x-2}}{1+\frac{4}{\left(x+2\right)\left(x-2\right)}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(x+2\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}.

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

Since \frac{\left(x+2\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)} and \frac{4}{\left(x+2\right)\left(x-2\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x+2\right)\left(x-2\right)+4.

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

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

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

Divide \frac{x^{2}}{x-2} by \frac{x^{2}}{\left(x+2\right)\left(x-2\right)} by multiplying \frac{x^{2}}{x-2} by the reciprocal of \frac{x^{2}}{\left(x+2\right)\left(x-2\right)}.

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

Cancel out \left(x-2\right)x^{2} in both numerator and denominator.

$$x+2$$