# How do you simplify sqrt (x-2) +5 / sqrt(x-2?

Jul 31, 2016

You need to put on a common denominator.

$= \frac{\sqrt{x - 2} \times \sqrt{x - 2} + 5}{\sqrt{x - 2}}$

$= \frac{x - 2 + 5}{\sqrt{x - 2}}$

$= \frac{x + 3}{\sqrt{x - 2}}$

You will want to rationalize the denominator now:

$= \frac{x + 3}{\sqrt{x - 2}} \times \frac{\sqrt{x - 2}}{\sqrt{x - 2}}$

$= \frac{\left(x + 3\right) \left(\sqrt{x - 2}\right)}{x - 2}$

Hopefully this helps!