Question

Simplify and rationalise the denominator of $\frac{6-4\sqrt{2}}{6+4\sqrt{2}}$

Answer 1

$\frac{6-4\sqrt{2}}{6+4\sqrt{2}}+\frac{(6-4\sqrt{2})}{(6-4\sqrt{2})}$

$\Rightarrow \frac{(6-4\sqrt{2}{)}^2}{(6{)}^2-(4\sqrt{2}{)}^2}$

$\Rightarrow \frac{36+32-48\sqrt{2}}{36-32}$

$=\frac{68-48\sqrt{2}}{4}$

$=17-12\sqrt{2}$.