Question

Rationalise the denominator and simplify:
$\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$

Answer 1

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

$=\frac{\sqrt{9}+\sqrt{6}+\sqrt{6}+\sqrt{4}}{\sqrt{9}-\sqrt{4}}$

$=\frac{3+2\sqrt{6}+2}{3-2}$

$=\frac{5+2\sqrt{6}}{1}$