Question
Evaluate $\frac{2^{\text{n}}+2^{\text{n}-1}}{2^{\text{n}+1}-2^{\text{n}}}.$
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Answer
$\frac{2^{\text{n}}+2^{\text{n}-1}}{2^{\text{n}+1}-2^{\text{n}}}$ $=\frac{2^{\text{n}-1}(2+1)}{2^{\text{n}}(2-1)}$ $=\frac{2^{\text{n}-1}\times3}{2^{\text{n}}\times1}$ $=\frac{3}{2^{\text{n}-\text{n}+1}}$ $=\frac{3}{2}$
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