Question 6

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Jambmaths question: 

Simplify $\frac{3({{2}^{n+1}})-4({{2}^{n-1}})}{{{2}^{n+1}}-{{2}^{n}}}$

Option A: 

2n + 1

Option B: 

2n – 1

Option C: 

4

Option D: 

¼

Jamb Maths Solution: 

$\begin{align}  & \frac{3({{2}^{n+1}})-4({{2}^{n-1}})}{{{2}^{n+1}}-{{2}^{n}}}=\frac{3({{2}^{n}}\cdot {{2}^{1}})-4({{2}^{n}}\cdot {{2}^{-1}})}{{{2}^{n}}\cdot 2-{{2}^{n}}} \\ & =\frac{{{2}^{n}}(3\cdot {{2}^{1}})-{{2}^{n}}(4\cdot {{2}^{-1}})}{{{2}^{n}}(2-1)} \\ & =\frac{{{2}^{n}}(6)-{{2}^{n}}(2)}{{{2}^{n}}} \\ & =\frac{{{2}^{n}}(6-2)}{{{2}^{n}}} \\ & =4 \end{align}$

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