Solve -x/-x-1+x/x-1=

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

Evaluate

$$-\frac{2x^{2}}{1-x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of -x-1 and x-1 is \left(-x-1\right)\left(x-1\right). Multiply \frac{-x}{-x-1} times \frac{x-1}{x-1}. Multiply \frac{x}{x-1} times \frac{-x-1}{-x-1}.

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

Since \frac{\left(-x\right)\left(x-1\right)}{\left(-x-1\right)\left(x-1\right)} and \frac{x\left(-x-1\right)}{\left(-x-1\right)\left(x-1\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(-x\right)\left(x-1\right)+x\left(-x-1\right).

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

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

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

Expand \left(-x-1\right)\left(x-1\right).

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

Multiply -1 and -1 to get 1.

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

Combine -x and x to get 0.

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

Multiply x and x to get x^{2}.

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

Factor

$$-\frac{2x^{2}}{1-x^{2}}$$