MCQ
$\frac{5^{\text{n}+2}-6\times5^{\text{n}+1}}{13\times5^\text{n}-2\times5^{\text{n}+1}}$ is equal to:
- A$\frac{5}{3}$
- ✓$-\frac{5}{3}$
- C$\frac{3}{5}$
- D$-\frac{3}{5}$
✓
Answer
Correct option: B.
$-\frac{5}{3}$
We have to simplify $\frac{5^{\text{n}+2}-6\times5^{\text{n}+1}}{13\times5^\text{n}-2\times5^{\text{n}+1}}$
Taking $5^n$ as a common factor we get
$\frac{5^{\text{n}+2}-6\times5^{\text{n}+1}}{13\times5^\text{n}-2\times5^{\text{n}+1}}=\frac{5^\text{n}(5^2-6\times5^1)}{5^\text{n}(13-2\times5^1)}$
$=\frac{5^\text{n}(25-30)}{5^\text{n}(13-10)}$
$=\frac{-5}{3}$
Taking $5^n$ as a common factor we get
$\frac{5^{\text{n}+2}-6\times5^{\text{n}+1}}{13\times5^\text{n}-2\times5^{\text{n}+1}}=\frac{5^\text{n}(5^2-6\times5^1)}{5^\text{n}(13-2\times5^1)}$
$=\frac{5^\text{n}(25-30)}{5^\text{n}(13-10)}$
$=\frac{-5}{3}$
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