462 Вправа 462Алгебра 8 клас Бевз 2025 · § 9 · стор. 93

462. Скоротіть дріб (n — ціле число).

а) ${\displaystyle \frac{4^{n+2}-4^n}{15}=}$${\displaystyle \frac{4^n(16-1)}{15}=}$${\displaystyle \frac{4^n\cdot \cancel{15}}{\cancel{15}}=}$${\displaystyle 4^n}$;

б) ${\displaystyle \frac{5^{n+1}+5^{n+3}}{26}=}$${\displaystyle \frac{5^{n+1}(1+25)}{26}=}$${\displaystyle \frac{5^{n+1}\cdot \cancel{26}}{\cancel{26}}=}$${\displaystyle 5^{n+1}}$;

в) ${\displaystyle \frac{3^n+1}{3^{-n}+1}=}$${\displaystyle \frac{3^n+1}{\frac{1}{3^n}+1}=}$${\displaystyle \frac{(3^n+1)\cdot 3^n}{1+3^n}=}$${\displaystyle 3^n}$;

г) ${\displaystyle \frac{6^{-n}+6^n}{36^n+1}=}$${\displaystyle \frac{\frac{1+6^{2n}}{6^n}}{36^n+1}=}$${\displaystyle \frac{\cancel{1+36^n}}{6^n\cancel{\left(36^n+1\right)}}=}$${\displaystyle 6^{-n}}$.