# How do you add or subtract (x^2)/(x-1)-(1)/(x-1)?

May 22, 2015

When you have fractions that have the same denominator, you simply add/subtract the numerators.

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

But note that if we check the roots for the numerator, we'll end up factoring it:

${x}^{2} - 1 = 0$
${x}^{2} = 1$
$x = \pm 1$ => $\left(x + 1\right) \left(x - 1\right)$

Rewriting:

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

Thus, your final answer for this subtraction is $x + 1$