Упр.247 ГДЗ Макарычев Миндюк Феоктистов 8 класс (Алгебра)

1. $$25^{-1}\cdot(5^{-1}+3^{-1})^{-2} =\frac{1}{25}\cdot\left(\frac{1}{5}+\frac{1}{3}\right)^{-2} =\frac{1}{25}\cdot\left(\frac{8}{15}\right)^{-2} =\frac{1}{25}\cdot\left(\frac{15}{8}\right)^2 =\frac{9}{64}$$
2. $$3^{-2}:\left(6^{-1}-3^{-1}\right)^2 =\frac{1}{9}:\left(\frac{1}{6}-\frac{1}{3}\right)^2 =\frac{1}{9}:\left(-\frac{1}{6}\right)^2 =\frac{1}{9}:\frac{1}{36} =4$$
3. $$\left(2^{-1}+3^{-1}\right)^2:\left(2^{-1}-3^{-1}\right)^2 =\left(\frac{1}{2}+\frac{1}{3}\right)^2:\left(\frac{1}{2}-\frac{1}{3}\right)^2 =\left(\frac{5}{6}\right)^2:\left(\frac{1}{6}\right)^2 =\frac{25}{36}:\frac{1}{36} =25$$
4. $$\left(12^{-1}+18^{-1}\right):\left(12^{-1}-18^{-1}\right) =\left(\frac{1}{12}+\frac{1}{18}\right):\left(\frac{1}{12}-\frac{1}{18}\right) =\frac{5}{36}:\frac{1}{36} =5$$

Ответ: $$\frac{9}{64};\ 4;\ 25;\ 5.$$