Question

plz answer my question .simplify by rationalizing denominator

Answer 1

Hope my answer helps you

Answer 2

Answer-

Simplifying the expression, its value came out to be 0

Solution-

The given expression is,

$=\frac{2}{\sqrt{5}+ \sqrt{3}}+\frac{1}{\sqrt{2}+ \sqrt{3}}-\frac{3}{\sqrt{5}+\sqrt{2}}$

$=\frac{2(\sqrt{5}- \sqrt{3})}{(\sqrt{5}+ \sqrt{3})(\sqrt{5}- \sqrt{3})}+\frac{1(\sqrt{2}- \sqrt{3})}{(\sqrt{2}+ \sqrt{3})(\sqrt{2}- \sqrt{3})}-\frac{3(\sqrt{5}- \sqrt{2})}{(\sqrt{5}+\sqrt{2})(\sqrt{5}- \sqrt{2})}$

$=\frac{2(\sqrt{5}- \sqrt{3})}{2}+\frac{1(\sqrt{2}- \sqrt{3})}{-1}-\frac{3(\sqrt{5}- \sqrt{2})}{3}$

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

$=\sqrt{5}- \sqrt{3}-\sqrt{2}+\sqrt{3}-\sqrt{5}+ \sqrt{2}$

$=0$