Question

simplify : 2√6/√2+√3 + 6√2/√6+√3 - 8√3/√6+√2​

Answer 1

Step-by-step explanation:

$\scriptsize\frac{2 \sqrt{6} }{ \sqrt{2} } + \sqrt{3} + \frac{6 \sqrt{2} }{ \sqrt{6} } + \sqrt{3} - \frac{8 \sqrt{3} }{ \sqrt{6} } + \sqrt{2}$

$\scriptsize \frac{2 \sqrt{6} }{ \sqrt{2} } - \frac{8 \sqrt{3} }{ \sqrt{6} } + \frac{6 \sqrt{2} }{ \sqrt{6} } + \sqrt{3}+ \sqrt{3} + \sqrt{2}$

$\frac{2 \sqrt{6} }{ \sqrt{2} } - \frac{8 \sqrt{3} + 6 \sqrt{2}}{ \sqrt{6} } + 2\sqrt{3}+ \sqrt{2}$

$\scriptsize\frac{2 \sqrt{6} }{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } - \frac{8 \sqrt{3} + 6 \sqrt{2}}{ \sqrt{6} } \times \frac{ \sqrt{6} }{ \sqrt{6} } + 2\sqrt{3}+ \sqrt{2}$

$\scriptsize\frac{2 \sqrt{12} }{ {2} } - \frac{\sqrt{6}(8 \sqrt{3} + 6 \sqrt{2})}{ {6} } + 2\sqrt{3}+ \sqrt{2}$

$\scriptsize\frac{2 \sqrt{12} }{ {2} } - \frac{8 \sqrt{18} + 6 \sqrt{12}}{ {6} } + 2\sqrt{3}+ \sqrt{2}$

$\scriptsize\frac{2 \times \sqrt{4} \times \sqrt{3} }{ {2} } - \frac{8 \times \sqrt{9} \times \sqrt{2} + 6 \times \sqrt{4} \times \sqrt{3} }{ {6} } + 2\sqrt{3}+ \sqrt{2}$

$\scriptsize\frac{2 \times 2 \times \sqrt{3} }{ {2} } - \frac{8 \times 3 \times \sqrt{2} + 6 \times 2 \times \sqrt{3} }{ {6} } + 2\sqrt{3}+ \sqrt{2}$

$\scriptsize\frac{4 \times \sqrt{3} }{ {2} } - \frac{24\times \sqrt{2} + 12 \times \sqrt{3} }{ {6} } + 2\sqrt{3}+ \sqrt{2}$

$\scriptsize\frac{4 \times \sqrt{3} }{ {2} } - \frac{12(2 \sqrt{2} + \sqrt{3} )}{ {6} } + 2\sqrt{3}+ \sqrt{2}$

$\scriptsize\frac{ \cancel4 \times \sqrt{3} }{ { \cancel2} } - \frac{ \cancel{12}(2 \sqrt{2} + \sqrt{3} )}{ { \cancel6} } + 2\sqrt{3}+ \sqrt{2}$

$\scriptsize2 \sqrt{3} - 2 (\sqrt{2} + \sqrt{3}) + 2 \sqrt{3} + \sqrt{2}$

$\scriptsize2 \sqrt{3} - 2 \sqrt{2} + 2 \sqrt{3} + 2 \sqrt{3} + \sqrt{2}$

$\scriptsize2 \sqrt{3} + 2 \sqrt{3} + 2 \sqrt{3} + \sqrt{2} - 2 \sqrt{2}$

$6 \sqrt{3} - \sqrt{2}$

I hope it is helpful