Question

Simplify 2√2-√3 --------------- √2+√3

Answer 1

Step-by-step explanation:

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

$= \frac{2 \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} }$

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

$= \frac{2(2 - \sqrt{6} - \sqrt{6} - 3) }{2 - 3}$

$= \frac{2( - 1 - 2 \sqrt{6} )}{ - 1}$

$= \frac{ - 2(1 + 2 \sqrt{6} )}{ - 1}$

$= 2(1 + 2 \sqrt{6} )$

$= 2 + 4 \sqrt{6}$