Question

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

Answer 1

$$\begin{gathered} \frac{2^n+2^{n-1}}{2^{n+1}-2^n} \\ =\frac{2^n\left(1+2^{-1}\right)}{2^n\left(2-1\right)} \\ =\frac{\left(1+{\displaystyle \frac{1}{2}}\right)}{1} \\ =\frac{2+1}{2} \\ =\frac{3}{2} \end{gathered}$$