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

$\frac{\left(3 x - 2\right) \sqrt{x - 1}}{x - 1}$
First of all you need to know that ${x}^{-} n = \frac{1}{x} ^ n$ and ${x}^{\frac{1}{m}} = \sqrt[m]{x}$.
so $x {\left(x - 1\right)}^{- \frac{1}{2}} + 2 {\left(x - 1\right)}^{\frac{1}{2}} = \frac{x}{\sqrt{x - 1}} + 2 \sqrt{x - 1} = \frac{x + 2 \sqrt{x - 1} \sqrt{x - 1}}{\sqrt{x - 1}} = \frac{x + 2 \left(x - 1\right)}{\sqrt{x - 1}} = \frac{x + 2 x - 2}{\sqrt{x - 1}} = \frac{3 x - 2}{\sqrt{x - 1}} = \left(3 x - 2\right) {\left(x - 1\right)}^{- \frac{1}{2}}$
You can stop here but usually you don't want a square root as a denominator so u multiply for sqrt(x-1)/sqrt(x-1:
$\frac{3 x - 2}{\sqrt{x - 1}} \cdot \frac{\sqrt{x - 1}}{\sqrt{x - 1}} = \frac{\left(3 x - 2\right) \sqrt{x - 1}}{x - 1}$