Solve x/1-x^2-x/1-x

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

Evaluate

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

Short Solution Steps

Factor 1-x^{2}.

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

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

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

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

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

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

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

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

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

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

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

Factor

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