Question

Rationalize the denominator-
(3√2-2√3)/(3√2+2√3)+(√12)/(√3-√2)

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Answer 1

Answer:

$\frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } \times \frac{3 \sqrt{2} - 2 \sqrt{3} }{ 3 \sqrt{2} - 2 \sqrt{3}} = \frac{18 - 12 \sqrt{6} + 12}{18 - 12} \\ \frac{6(1 - 2 \sqrt{6}) }{6} = 1 - 2 \sqrt{6}$

and second one,

$\frac{ \sqrt{12} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } = \frac{ \sqrt{36} + \sqrt{24} }{3 - 2} = \frac{6 + 2 \sqrt{6} }{1 } \\ 2(3 + \sqrt{6} )$

adding these two,

$(1 - 2 \sqrt{6} ) + 2(3 + \sqrt{6} ) \\ = 1 + 6 \\ = 7$