Question

Simplifique a expressão, usando sempre que possível as propriedades da potência:
3^n-2 -3^n / 3^n+1 + 3^n-1

Answer 1

Ola Diaws

(3^(n-2) - 3^n)/(3^(n+1) + 3^(n-1)) 

3^n*(1/9 - 1)/3^n*(3 + 1/3) = 

(1/9 - 1)/(3 + 1/3) = (-8/9)/(10/3) = (-8/9)*(3/10) = -4/15 

Answer 2

AE VELHO,

use as propriedades da exponenciação..

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$a^{-1}= \dfrac{1}{a^1} = \dfrac{1}{a} \\\\ a^{m+n}=a^m\cdot a^n$

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$\dfrac{3^{n-2}-3^n}{3^{n+1}+3^{n-1}}\Rightarrow \dfrac{3^n\cdot3^{-2}-3^n}{3^n\cdot3^1+3^n\cdot3^{-1}}\Rightarrow \dfrac{3^n\cdot(3^{-2} -1)}{3^n\cdot(3^1+3^{-1})} \\\\\\ \Rightarrow\dfrac{\not3^n\cdot(3^{-2} -1)}{\not3^n\cdot(3^1+3^{-1})}\Rightarrow \dfrac{ \dfrac{1}{9} -1}{3+ \dfrac{1}{3} }\Rightarrow \dfrac{- \dfrac{8}{9} }{ \dfrac{10}{3} }\\\\\\ \Rightarrow \left(-\dfrac{8}{9}\right)\div \dfrac{10}{3}\Rightarrow\left(- \dfrac{8}{9} \right)\times \dfrac{3}{10}\Rightarrow -\dfrac{24}{90}$

$-\dfrac{24\div6}{90\div6}\Rightarrow \Large\boxed{- \dfrac{4}{15}}$

valeu manu!