Question

Solve:-
$\frac{\sqrt{5}+\sqrt{3}}{2\sqrt{5}-3\sqrt{3}}=a-b\sqrt{15}$

Answer 1

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

$=\frac{2.5+3\sqrt{15}+2\sqrt{15}+9}{(2\sqrt{5}{)}^2-(3\sqrt{3}{)}^2}$

$=\frac{19+5\sqrt{15}}{20-27}=\frac{-19}{7}-\frac{5}{7}\sqrt{15}$

$=a-b\sqrt{15}$

$\therefore a=\frac{-19}{7},b=\frac{5}{7}$.