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