Question

rationalize the denominator of 5+root2 / 3-root3

Answer 1

$\huge\mathfrak\green{ANSWER}$

see image for explanation and have a great day friend

Answer 2

$\huge \bf{ \frac{5 + \sqrt{2} }{3 - \sqrt{3} } \: \: \: \: \: \: \:}\\ \\ \\ \\ \tt{ \implies \: \frac{5 + \sqrt{2} }{3 - \sqrt{3} } \times \frac{3 + \sqrt{3} }{3 + \sqrt{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \ \tt{ \implies \frac{(5 \times 3) +( 5 \times \sqrt{3}) + (\sqrt{2 }\times 3 ) + ( \sqrt{2} \times \sqrt{3}) }{( {3})^{2} - (\sqrt{3} )^{2} } } \\ \\ \\ \tt{ \implies} \frac{15 + 5 \sqrt{3 } + 3 \sqrt{2 } + \sqrt{6} }{6} \: \: \: \: \: \: \: \: \: \:$