# How do you combine  1/(x-1) - x/(x^2+1)?

Use the common denominator $\left(x - 1\right) \left({x}^{2} + 1\right)$ and get:
$\frac{1}{x - 1} - \frac{x}{{x}^{2} + 1} = \frac{{x}^{2} + 1 - x \left(x - 1\right)}{\left(x - 1\right) \left({x}^{2} + 1\right)} =$
$= \frac{\cancel{{x}^{2}} + 1 \cancel{- {x}^{2}} + x}{\left(x - 1\right) \left({x}^{2} + 1\right)} = \frac{x + 1}{\left(x - 1\right) \left({x}^{2} + 1\right)}$