Question

Сократите дробь:

1)(3^n+3^(-n))/(9^n+1)
2)(5^(n+1)-5^n)/4
3)(((4^n+4^(n-1))^2)/4^(2n-2)

Answer 1

$\dfrac{3^n+3^{-n}}{9^n+1}=\dfrac{3^{-n}*(3^{2n}+1)} {9^n+1}=\dfrac{3^{-n}*(9^n+1)} {9^n+1}=3^{-n}=\dfrac{1}{3^n}$

$\dfrac{5^{n+1}-5^n}{4}=\dfrac{5^{n}*5-5^n} {4}=\dfrac{5^n*(5-1)} {4}=\dfrac{5^n*4} {4}=5^n$

$\dfrac{(4^n+4^{n-1})^2}{4^{2n-2}}=\dfrac{[4^{n-1}(4+1)]^2}{4^{2n-2}}=\dfrac{4^{2n-2}*5^2}{4^{2n-2}}=25$