# How do you simplify \frac { \sqrt { x - 5} } { 3} - \frac { 2} { \sqrt { x - 5} }?

Aug 15, 2017

((x - 11) (sqrt (x - 5)))/(3(x - 5)

#### Explanation:

$\setminus \frac{\setminus \sqrt{x - 5}}{3} - \setminus \frac{2}{\setminus \sqrt{x - 5}}$

Taking L.C.M

$\Rightarrow \frac{\left(\sqrt{x - 5}\right) \left(\sqrt{x - 5}\right) - \left(2 \times 3\right)}{\left(3\right) \sqrt{x - 5}}$

$\Rightarrow \frac{{\sqrt{\left(x - 5\right)}}^{2} - 6}{3 \sqrt{x - 5}}$

$\Rightarrow \frac{x - 5 - 6}{3 \sqrt{x - 5}}$

$\Rightarrow \frac{x - 11}{3 \sqrt{x - 5}}$

$\Rightarrow \frac{x - 11}{3 \sqrt{x - 5}} \times \frac{\sqrt{x - 5}}{\sqrt{x - 5}}$

rArr ((x - 11) (sqrt (x - 5)))/(3sqrt (x - 5)^2

rArr ((x - 11) (sqrt (x - 5)))/(3 xx (x - 5)

rArr ((x - 11) (sqrt (x - 5)))/(3(x - 5)

Aug 15, 2017

$= \frac{x - 5 - 6 \sqrt{x - 5}}{3 \left(x - 5\right)}$

#### Explanation:

Before we subtract the fractions, let's change the second one so there is no radical in the denominator.

sqrt(x-5)/3 - 2/sqrt(x-5) xx sqrt(x-5)/sqrt(x-5)color(white)(xxxxx)color(blue)([ sqrt(x-5)/sqrt(x-5) =1]

$= \frac{\sqrt{x - 5}}{3} - \frac{2 \sqrt{x - 5}}{\left(x - 5\right)} \text{ } \leftarrow \left({\sqrt{x - 5}}^{2} = \left(x - 5\right)\right)$

=(sqrt(x-5)sqrt(x-5)" " -" " 3xx2sqrt(x-5))/(3(x-5)

$= \frac{x - 5 - 6 \sqrt{x - 5}}{3 \left(x - 5\right)}$