Question

please give its full solution it's very very urgent​

Answer 1

$\begin{gathered}\large {\boxed{\sf{\mid{\overline {\underline {\star ANSWER ::}}}\mid}}}\end{gathered}$

To Find :-

$\frac{ {2}^{n - 1} + {2}^{n} }{ {2}^{n + 2} - {2}^{n + 1} }$

Solution :-

TO KNOW :

$1. \: \boxed {\sf{ {a}^{m + n} = {a}^{m} \times {a}^{n} }} \\ 2. \: \boxed {\sf{ {a}^{m - n} = \frac{ {a}^{m} }{{a}^{n}} }}$

From the problem, using the formulae :

$\frac{ {2}^{n - 1} + {2}^{n} }{ {2}^{n + 2} - {2}^{n + 1} } \\ \\ = \frac{ {2}^{n}÷ {2}^{1} + {2}^{n} }{ {2}^{n} \times {2}^{2} - {2}^{n} \times {2}^{1} } \\ \\ = \frac{ {2}^{n} ( \frac{1}{2} + 1) }{ {2}^{n}( {2}^{2} - 2 )} \\ \\ = \frac{ \frac{3}{2} }{ 2 } \\ \\ \star \: \underline{\boxed {= \frac{3}{4} }} \: \star$

@SweetestBitter