Question

simplify 1/√3+√2-1/√2-√3​

Answer 1

GIVEN :–

$\\ = { \bold{ \dfrac{1}{ \sqrt{3} + \sqrt{2} } - \dfrac{1}{ \sqrt{2} - \sqrt{3}}}}$

TO FIND :–

• Simplified form = ?

SOLUTION :–

• Let the function –

$\\ \implies { \bold{x = \dfrac{1}{ \sqrt{3} + \sqrt{2} } - \dfrac{1}{ \sqrt{2} - \sqrt{3}}}}$

• Rationalization of denominator –

$\\ \implies { \bold{x = \dfrac{1}{ \sqrt{3} + \sqrt{2}} \times \dfrac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } - \left \{\dfrac{1}{ \sqrt{2} - \sqrt{3}} \times \dfrac{ \sqrt{2} + \sqrt{3} }{ \sqrt{2} + \sqrt{3} } \right \} }}$

$\\ \implies { \bold{x = \dfrac{ \sqrt{3} - \sqrt{2} }{ (\sqrt{3} + \sqrt{2})(\sqrt{3} - \sqrt{2}) } - \left \{ \dfrac{ \sqrt{2} + \sqrt{3} }{( \sqrt{2} - \sqrt{3})( \sqrt{2} + \sqrt{3}) } \right \} }}$

• Now Using –

$\\ \: \: \blacktriangleright \: \: \large { \boxed{ \bold{(a + b)(a - b) = {a}^{2} - {b}^{2} }}}$

• So that –

$\\ \implies { \bold{x = \dfrac{ \sqrt{3} - \sqrt{2} }{ (\sqrt{3})^{2} - ( \sqrt{2})^{2} } - \left \{ \dfrac{ \sqrt{2} + \sqrt{3} }{( \sqrt{2} )^{2} - ( \sqrt{3})^{2}} \right \} }}$

$\\ \implies { \bold{x = \dfrac{ \sqrt{3} - \sqrt{2} }{ 3 - 2} - \left \{ \dfrac{ \sqrt{2} + \sqrt{3} }{2 - 3} \right \} }}$

$\\ \implies { \bold{x = \dfrac{ \sqrt{3} - \sqrt{2} }{1} - \left \{ \dfrac{ \sqrt{2} + \sqrt{3} }{ - 1} \right \} }}$

$\\ \implies { \bold{x = { \sqrt{3} - \sqrt{2} } + { \sqrt{2} + \sqrt{3} }}}$

$\\ \implies \large{ \boxed { \bold{x = 2 \sqrt{3}}}}$

Answer 2

Answer:

I hope answer is helpful to us