Question

Rationalise the denominator and simplify:
$\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

Answer 1

$\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}=$$\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times$$\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}$ (Rationalising the denominator)

$=\frac{(\sqrt{5}+\sqrt{3}{)}^2}{5-3}$

$=\frac{5+3+2\sqrt{15}}{2}$

$=\frac{8+2\sqrt{15}}{2}$

$=4+\sqrt{15}$