$$\frac { x ^ { 2 } - 2 } { x - 1 } - \frac { x } { 1 - x }$$
Evaluate
$x+2$
Short Solution Steps
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x-1$ and $1-x$ is $x-1$. Multiply $\frac{x}{1-x}$ times $\frac{-1}{-1}$.
$$\frac{x^{2}-2}{x-1}-\frac{-x}{x-1}$$
Since $\frac{x^{2}-2}{x-1}$ and $\frac{-x}{x-1}$ have the same denominator, subtract them by subtracting their numerators.
$$\frac{x^{2}-2-\left(-x\right)}{x-1}$$
Do the multiplications in $x^{2}-2-\left(-x\right)$.
$$\frac{x^{2}-2+x}{x-1}$$
Factor the expressions that are not already factored in $\frac{x^{2}-2+x}{x-1}$.
$$\frac{\left(x-1\right)\left(x+2\right)}{x-1}$$
Cancel out $x-1$ in both numerator and denominator.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x-1$ and $1-x$ is $x-1$. Multiply $\frac{x}{1-x}$ times $\frac{-1}{-1}$.
$$\frac{x^{2}-2}{x-1}-\frac{-x}{x-1}$$
Since $\frac{x^{2}-2}{x-1}$ and $\frac{-x}{x-1}$ have the same denominator, subtract them by subtracting their numerators.
$$\frac{x^{2}-2-\left(-x\right)}{x-1}$$
Do the multiplications in $x^{2}-2-\left(-x\right)$.
$$\frac{x^{2}-2+x}{x-1}$$
Factor the expressions that are not already factored in $\frac{x^{2}-2+x}{x-1}$.
$$\frac{\left(x-1\right)\left(x+2\right)}{x-1}$$
Cancel out $x-1$ in both numerator and denominator.
