Question

\frac { 6 ^ { n + 2 } - 6 ^ { n } } { 6 ^ { n + 1 } + 6 ^ { n } }

Answer 1

Answer:

5

Step-by-step explanation:

Given expression:

$\dfrac{6^{n+2}-6^n}{6^{n+1}+6^n}$

$\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c$

$\implies \dfrac{6^n6^2-6^n}{6^n6^1+6^n}$

Factor:

$\implies \dfrac{6^n(6^2-1)}{6^n(6^1+1)}$

Cancel $6^n$ :

$\implies \dfrac{(6^2-1)}{(6^1+1)}$

Simplify:

$\implies \dfrac{36-1}{6+1}$

$\implies \dfrac{35}{7}$

$\implies 5$