Question

simplifique $\frac{ 3^{n+3} -3.3^{n} }{4. 3^{n+2} }$

Answer 1

$\dfrac{3^{n+3}-3\cdot3^{n}}{4\cdot3^{n+2}}$

Colocando 3^n em evidência no numerador e denominador:

$\dfrac{3^{n+3}-3\cdot3^{n}}{4\cdot3^{n+2}}=\dfrac{3^{n}\cdot(3^{3}-3)}{3^{n}\cdot(4\cdot3^{2})}\\\\\\\dfrac{3^{n+3}-3\cdot3^{n}}{4\cdot3^{n+2}}=\dfrac{3^{3}-3}{4\cdot3^{2}}\\\\\\\dfrac{3^{n+3}-3\cdot3^{n}}{4\cdot3^{n+2}}=\dfrac{3^{2}-1}{4\cdot3^{1}}\\\\\\\dfrac{3^{n+3}-3\cdot3^{n}}{4\cdot3^{n+2}}=\dfrac{9-1}{12}\\\\\\\dfrac{3^{n+3}-3\cdot3^{n}}{4\cdot3^{n+2}}=\dfrac{8}{12}\\\\\\\boxed{\boxed{\dfrac{3^{n+3}-3\cdot3^{n}}{4\cdot3^{n+2}}=\dfrac{2}{3}}}$