Solve x/2*x-2/x+2-1/frac{x+2{x-2}+1}=

$$\frac { x } { 2 } \cdot \frac { \frac { x - 2 } { x + 2 } - 1 } { \frac { x + 2 } { x - 2 } + 1 } =$$

Evaluate

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

Short Solution Steps

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

$$\frac{x}{2}\times \frac{\frac{x-2}{x+2}-\frac{x+2}{x+2}}{\frac{x+2}{x-2}+1}$$

Since \frac{x-2}{x+2} and \frac{x+2}{x+2} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{x}{2}\times \frac{\frac{x-2-x-2}{x+2}}{\frac{x+2}{x-2}+1}$$

Combine like terms in x-2-x-2.

$$\frac{x}{2}\times \frac{\frac{-4}{x+2}}{\frac{x+2}{x-2}+1}$$

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

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

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

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

Combine like terms in x+2+x-2.

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

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

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

Cancel out 2 in both numerator and denominator.

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

Multiply \frac{x}{2} times \frac{-2\left(x-2\right)}{x\left(x+2\right)} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2x in both numerator and denominator.

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

To find the opposite of x-2, find the opposite of each term.

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

The opposite of -2 is 2.

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

Expand

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

Short Solution Steps

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

$$\frac{x}{2}\times \frac{\frac{x-2}{x+2}-\frac{x+2}{x+2}}{\frac{x+2}{x-2}+1}$$

Since \frac{x-2}{x+2} and \frac{x+2}{x+2} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{x}{2}\times \frac{\frac{x-2-x-2}{x+2}}{\frac{x+2}{x-2}+1}$$

Combine like terms in x-2-x-2.

$$\frac{x}{2}\times \frac{\frac{-4}{x+2}}{\frac{x+2}{x-2}+1}$$

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

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

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

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

Combine like terms in x+2+x-2.

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

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

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

Cancel out 2 in both numerator and denominator.

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

Multiply \frac{x}{2} times \frac{-2\left(x-2\right)}{x\left(x+2\right)} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2x in both numerator and denominator.

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

To find the opposite of x-2, find the opposite of each term.

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

The opposite of -2 is 2.

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