Question

please answer this question.
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Answer 1

$\huge \bigstar \: \: \: \: \: \huge \tt \frac{ {2}^{n} + {2}^{( n- 1)} }{ {2}^{(n + 1)} - {2}^{n} } = \frac{3}{2} \\ \\ \\ \implies \large \tt \: \: \: 2 [{2}^{n} + {2}^{( n- 1)} ] = 3[ {2}^{(n + 1)} - {2}^{n} ] \\ \\ \implies \large \tt \: \: \: 2[ {2}^{n} (1 + {2}^{- 1} )] = 3[ {2}^{n}( {2}^{1} - 1) ] \\ \\ \implies \large \tt \: \: \: \: 2[ {2}^{n}(1 + \frac{1}{2} \bigg) \bigg] = 3[ {2}^{n}(2 - 1) ] \\ \\ \implies \large \tt \: \: \: \: \: \: { \cancel2}^{} \bigg[ {{2}^{n} } \bigg( \frac{3}{ \cancel2} \bigg) \bigg] = 3[{ {2}^{n}}(1) ] \\ \\ \implies \large \tt \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {2}^{n} \times 3 = 3 \times {2}^{n}$