Question

On simplification, the expression $\frac{5^{n+2}-6\times 5^{n+1}}{13\times 5^n-2\times 5^{n+1}}$ equals
(a) $\frac{5}{3}$

(b) $-\frac{5}{3}$

(c) $\frac{3}{5}$

(d) $-\frac{3}{5}$

Answer 1

$$\begin{gathered} \frac{5^{n+2}-6\times 5^{n+1}}{13\times 5^n-2\times 5^{n+1}} \\ =\frac{5^n\times 5^2-6\times 5^n\times 5}{13\times 5^n-2\times 5^n\times 5} \\ =\frac{5^n\times 5\left[5-6\right]}{5^n\left[13-2\times 5\right]} \\ =\frac{-5}{3} \end{gathered}$$
Hence, the correct answer is option (b).