What is (3^{n+1}+3^{n+2}+3^{n+3})/(3^{n-1)+3^{n-2}+3^{n-3}} ?

The solution to (3^{n+1}+3^{n+2}+3^{n+3})/(3^{n-1)+3^{n-2}+3^{n-3}} is 81

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simplify (3^{n+1}+3^{n+2}+3^{n+3})/(3^{n-1)+3^{n-2}+3^{n-3}}

simplify

\frac{3 ^{n + 1} + 3 ^{n + 2} + 3 ^{n + 3}}{3 ^{n - 1} + 3 ^{n - 2} + 3 ^{n - 3}}

81

Solution steps

\frac{3 ^{n + 1} + 3 ^{n + 2} + 3 ^{n + 3}}{3 ^{n - 1} + 3 ^{n - 2} + 3 ^{n - 3}}

Factor

3^{n + 1} + 3^{n + 2} + 3^{n + 3} : 3^{n + 1} \cdot 13

= \frac{3 ^{n + 1} \cdot 13}{3 ^{n - 1} + 3 ^{n - 2} + 3 ^{n - 3}}

Factor

3^{n - 1} + 3^{n - 2} + 3^{n - 3} : 3^{n - 3} \cdot 13

= \frac{3 ^{n + 1} \cdot 13}{3 ^{n - 3} \cdot 13}

Cancel the common factor:

13

= \frac{3 ^{n + 1}}{3 ^{n - 3}}

Simplify

\frac{3 ^{n + 1}}{3 ^{n - 3}} : 3^{4}

= 3^{4}

3^{4} = 81

= 81

- \frac{56}{( - 8 )}

\frac{x ^{2} y ^{2} - 9}{3 - x y}

\frac{x ^{2} + 2 x - 8}{x ^{2} - 16}

\frac{t ^{2} - 5 t + 6}{t ^{2} - t - 2}

x^{2} + x - 110

What is (3^{n+1}+3^{n+2}+3^{n+3})/(3^{n-1)+3^{n-2}+3^{n-3}} ?
The solution to (3^{n+1}+3^{n+2}+3^{n+3})/(3^{n-1)+3^{n-2}+3^{n-3}} is 81