Question

Como resolver??$\frac{2 ^{n+3} + 2 ^{n+2} + 2 ^{n-1}}{2^{n-2} + 2^{n-1} }$

Answer 1

$\\ = \frac{2^n^+^3+2^n^+^2+2^n^-^1}{2^n^-^2+2^n^-^1} \\ \\ = \frac{2^n2^3+2^n2^2+2^n2^-^1}{2^n2^-^2+2^n2^-^1} \\ \\ = \frac{2^n(2^3+2^2+2^-^1)}{2^n(2^-^2+2^-^1)} \\ \\ = \frac{2^3+2^2+2^-^1}{2^-^2+2^-^1} \\ \\ = \frac{8+4+ \frac{1}{2} }{ \frac{1}{4}+ \frac{1}{2} } \\ \\ = \frac{12+ \frac{1}{2} }{ \frac{2*1+4*1}{4*2} } \\ \\ = \frac{ \frac{12*2+1}{2} }{ \frac{6}{8} } \\ \\ = \frac{25}{2} * \frac{8}{6} \\ \\ = \frac{25}{2}* \frac{4}{3}$

$\\ = \frac{100}{6} \\ \\ = \frac{50}{3}$