Question

(Ulbra-RS) A expressão
$\frac{ {3}^{3 + x} - {3}^{x - 3} }{ {3}^{x} + {3}^{x - 3} }$
é igual a:
a)3^×
b)3^-×
c)3^-3
d)26
e)28

Answer 1

$\textbf{Algumas propriedades de potencia\c{c}\~ao:}\\\\ \mathrm{\Rightarrow a^m.a^n=a^{m+n}\ \ \bigg\|\ \ \Rightarrow \dfrac{a^m}{a^n}=a^{m-n}}\\\\ \textbf{Resolu\c{c}\~ao:}\\\\ \mathrm{\dfrac{3^{3+x}-3^{x-3}}{3^x+3^{x-3}}=\dfrac{3^3.3^x-\dfrac{3^x}{3^3}}{3^x+\dfrac{3^x}{3^3}}=\dfrac{3^x\bigg(27-\dfrac{1}{27}\bigg)}{3^x\bigg(1+\dfrac{1}{27}\bigg)}=}\\\\ \mathrm{=\dfrac{\dfrac{27.27-1}{27}}{\dfrac{27+1}{27}}=\dfrac{729-1}{27}.\dfrac{27}{28}=\dfrac{728}{28}=\boxed{\mathbf{26}}}$