Question

pls answer these 2 questions fast. Best answer will definitely be marked the brainliest

Answer 1

hope this helps you... tell me if it's tight and Mark it as brainliest

Answer 2

Hey friend,
Here is the answer you were looking for:
$1) \frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} } \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{2 \times 2 \times 2 \times 2 \times 3} + { \sqrt{2 \times 3 \times 3} }{?} } \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{2 \times 2 \sqrt{3} + 3 \sqrt{2} } \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \times \frac{4 \sqrt{3} - 3 \sqrt{2} }{4 \sqrt{3} - 3 \sqrt{2} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{7 \sqrt{3} \times 4 \sqrt{3} - 7 \sqrt{3} \times 3 \sqrt{2} - 5 \sqrt{2} \times 4 \sqrt{3} + 5 \sqrt{2} \times 3 \sqrt{2} }{ {(4 \sqrt{3} )}^{2} - {(3 \sqrt{2}) }^{2} } \\ \\ = \frac{84 - 21 \sqrt{6} - 20 \sqrt{6} + 30 }{48 - 18} \\ \\ = \frac{114 - 41 \sqrt{6} }{30} \\ \\ 2) \frac{2 \sqrt{6} - \sqrt{5} }{3 \sqrt{5} - 2 \sqrt{6} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \: \\ \\ = \frac{2 \sqrt{6} - \sqrt{5} }{3 \sqrt{5} - 2 \sqrt{6} } \times \frac{3 \sqrt{5} + 2 \sqrt{6} }{3 \sqrt{5} + 2 \sqrt{6} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{2 \sqrt{6} \times 3 \sqrt{5} + 2 \sqrt{6} \times 2 \sqrt{6} - \sqrt{5} \times 3 \sqrt{5} - \sqrt{5} \times 2 \sqrt{6} }{ {(3 \sqrt{5} )}^{2} - {(2 \sqrt{6} )}^{2} } \\ \\ = \frac{6 \sqrt{30} + 24 - 15 - 2 \sqrt{30} }{ 45 - 24 } \\ \\ = \frac{4 \sqrt{30} + 9 }{21}$


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Hope this helps!!!!

@Mahak24

Thanks....
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