Question

Rationalize the following :
$\frac{2}{ \sqrt{3} - \sqrt{5} }$
anyone please answer this by step by step ​

Answer 1

Step-by-step explanation:

pls go through the image and u will get to understand.......

HOPE IT HELPS.....

Answer 2

$\frac{2\left(\sqrt{3}+\sqrt{5}\right)}{\left(\sqrt{3}-\sqrt{5}\right)\left(\sqrt{3}+\sqrt{5}\right)}$Answer:

$\frac{2}{\sqrt{3}-\sqrt{5}}=-\sqrt{3}-\sqrt{5}\quad \left(\mathrm{Decimal:\quad }\:-3.96811\dots \right)$

Steps

$\frac{2}{\sqrt{3}-\sqrt{5}}$

$\mathrm{Multiply\:by\:the\:conjugate}\:\frac{\sqrt{3}+\sqrt{5}}{\sqrt{3}+\sqrt{5}}$

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

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

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}$

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

$\mathrm{Divide\:the\:numbers:}\:\frac{2}{2}=1$

$-\left(\sqrt{3}+\sqrt{5}\right)$

distribute  paranthesis

$-\left(\sqrt{3}\right)-\left(\sqrt{5}\right)$

$\mathrm{Apply\:minus-plus\:rules}$

$+(-a)=-a$

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