Question

write answer with steps i want to know the exponent value

Answer 1

HOPE IT WILL HELP YOU

Answer 2

Hey here is your answer
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$= \frac{ \sqrt{5} + \sqrt{3} }{2 \sqrt{5} - 3 \sqrt{3} } = a - b \sqrt{15} \\ \\ lhs. \\ \\ = \frac{ \sqrt{5} + \sqrt{3} }{2 \sqrt{5} - 3 \sqrt{3} } \\ \\ = \frac{ \sqrt{5} + \sqrt{3} }{2 \sqrt{5} - 3 \sqrt{3} } \times \frac{2 \sqrt{5} + 3 \sqrt{3} }{2 \sqrt{5} + 3 \sqrt{3} } \\ \\ = \frac{10 + 3 \sqrt{15} + 2 \sqrt{15} + 9 }{ {(2 \sqrt{5}) }^{2} - {(3 \sqrt{3}) }^{2} } \\ \\ = \frac{19 + 5 \sqrt{15} }{20 - 27} \\ \\ = \frac {19 + 5 \sqrt{15}}{-7} \\ \\ comparing \: lhs \: and \: rhs \: we \: get \\ \\ = \frac {19 + 5 \sqrt{15}}{-7} = a - b \sqrt{15} \\ \\ where \: . \\ \\ a = \frac {-19}{7} \\ \\ b = \frac { 5}{7}$
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