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