Question

Solve the following in attachment​

Answer 1

$(a). \: \frac{3}{4 - \sqrt{3} } + \frac{2}{4 + \sqrt{3} }$

$\: \: \: \: \: \frac{3(4 + \sqrt{3} ) +2(4 - \sqrt{3}) }{ {4}^{2} - { \sqrt{3} }^{2} }$

$\: \: \: \: \: \frac{12 + 3 \sqrt{3} + 8 - 2 \sqrt{3} }{16 - 3}$

$\: \: \: \: \: \frac{20 + \sqrt{3} }{13}$

$(b). \: \frac{2 \sqrt{3} }{ \sqrt{3} - \sqrt{2} } + \frac{3 \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

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

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

$\: \: \: \: \: 5 \sqrt{6}$