Question

Find the value... please​

Answer 1

Answer:

$\frac{ \sqrt{5} + 7 \sqrt{2} }{3} - 2 \sqrt{3}$

Step-by-step explanation:

Rationalising the first term

$\frac{2}{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ \\ \frac{2( \sqrt{5} + \sqrt{3}) }{5 - 3} = \frac{2( \sqrt{5} + \sqrt{3} )}{2} \: \: (cancle \: 2)$

Rationalising the second term

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

Rationalising the third term

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

Now,

$\sqrt{5} + \sqrt{3} - 3( \sqrt{3} - \sqrt{2} ) - \frac{2( \sqrt{5} + \sqrt{2} )}{3} \\ \\ \sqrt{5 } + \sqrt{3} - 3 \sqrt{3} + 3 \sqrt{2} - \frac{2 \sqrt{5} + 2 \sqrt{2} }{3} \\ \\ 5 - 2 \sqrt{3} + 3 \sqrt{2} - \frac{ - 2 \sqrt{5} + 2 \sqrt{2} }{3} \\ \\ \frac{3 \sqrt{5} + 9 \sqrt{2} - (2 \sqrt{5} + 2 \sqrt{2}) }{3} - 2 \sqrt{3} \\ \\ \frac{3 \sqrt{5} + 9 \sqrt{2} - 2 \sqrt{5} - 2 \sqrt{2} }{3} - 2 \sqrt{3} \\ \\ \frac{ \sqrt{5 } + 7 \sqrt{2} }{3} - 2 \sqrt{3}$