How do you simplify (3-3sqrt(3a))/(4sqrt(8a))?

Nov 17, 2017

$\frac{3 \sqrt{2 a}}{16 a} - \frac{3 \sqrt{6}}{16}$

Explanation:

$\frac{3 - 3 \sqrt{3 a}}{4 \sqrt{8 a}}$

Multiply both denominator and numerator by $\sqrt{8 a}$,
$\frac{3 - 3 \sqrt{3 a}}{4 \sqrt{8 a}} \times \frac{\sqrt{8 a}}{\sqrt{8 a}}$
$= \frac{3 \sqrt{8 a} - 3 \sqrt{24 {a}^{2}}}{32 a}$
$= \frac{6 \sqrt{2 a} - 6 a \sqrt{6}}{32 a}$
$= \frac{3 \sqrt{2 a} - 3 a \sqrt{6}}{16 a}$
$= \frac{3 \sqrt{2 a}}{16 a} - \frac{3 \sqrt{6}}{16}$