# How do you rationalize the denominator and simplify 1/(sqrtx-1)?

May 3, 2016

$\frac{\sqrt{x} + 1}{x - 1}$ for $x \ge 0$ anmd $x \ne 1$.

#### Explanation:

The domain of this function is:
$x \ge 0$ to be able to perform an operation $\sqrt{x}$,
$\sqrt{x} - 1 \ne 0$, that is $x \ne 1$ to avoid division by $0$.

For all $x$ satisfying the above criteria let's multiply both numerator and denominator by the same expression $\left(\sqrt{x} + 1\right)$.

This transforms our expression into
$\frac{\sqrt{x} + 1}{\left(\sqrt{x} - 1\right) \cdot \left(\sqrt{x} + 1\right)} = \frac{\sqrt{x} + 1}{x - 1}$