Question

Rational the denominator & simplify:-
$\frac{\sqrt{3}+1}{2\sqrt{2}-\sqrt{3}}$

Answer 1

Rationalizing the denominator of $\frac{\sqrt{3}+1}{2\sqrt{2}-\sqrt{3}}$.

$\frac{\sqrt{3}+1}{2\sqrt{2}-\sqrt{3}}\times \frac{\left(2\sqrt{2}+\sqrt{3}\right)}{\left(2\sqrt{2}+\sqrt{3}\right)}$

$=\frac{\left(\sqrt{3}+1\right)\left(2\sqrt{2}+\sqrt{3}\right)}{{\left(2\sqrt{2}\right)}^2-{\left(\sqrt{3}\right)}^2}$

$=\frac{2\sqrt{6}+3+2\sqrt{2}+\sqrt{3}}{8-3}$

$=\frac{2\left(\sqrt{6}+\sqrt{2}\right)+\sqrt{3}+3}{5}$