Question

3 root 2-2 root 3/3 root 2+2 root 3+root 12/root 3-root 2
simplify the following by rationalizing the denominator

Answer 1

Heya there !!!
Here is the answer you were looking for:
$\frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } + \frac{ \sqrt{12} }{ \sqrt{3} - \sqrt{2} } \\ \\ = \frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } - \frac{ \sqrt{2 \times 2 \times 3} }{ \sqrt{3} - \sqrt{2} } \\ \\ = \frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } - \frac{2 \sqrt{3} }{ \sqrt{3} - \sqrt{2} }$

On rationalizing the denominators we get,

$= \frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } \times \frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } - \frac{2 \sqrt{3} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ \\ = \frac{ {(3 \sqrt{2} )}^{2} + {(2 \sqrt{3} )}^{2} + 2(3 \sqrt{2} )(2 \sqrt{3}) }{ {(3 \sqrt{2}) }^{2} - {(2 \sqrt{3}) }^{2} } - \frac{2 \sqrt{3}( \sqrt{3} + \sqrt{2} ) }{ {( \sqrt{3} )}^{2} - {( \sqrt{2} )}^{2} } \\ \\ = \frac{18 + 12 + 12 \sqrt{6} }{18 - 12} - \frac{6 - 2 \sqrt{6} }{3 - 2} \\ \\ = \frac{30 + 12 \sqrt{6} }{6} - 6 + 2 \sqrt{6} \\ \\ = 5 +2 \sqrt{6} - 6 + 2 \sqrt{6} \\ \\ = - 1 + 4 \sqrt{6} \\ \\ = 4 \sqrt{6} - 1$

Hope this helps!!!

If you have any doubt regarding to my answer, feel free to ask me in the comment section ^_^

@Mahak24

Thanks...
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Answer 2

Answer:

here it's your correct answer = 11

hope u be happy with this answer.

any doubt than comment me .

OK !

: ) : ) . . . . . . .