Решебник по алгебре 8 класс Мерзляк Задание 111

\[\boxed{\text{111\ (111).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ a^{\backslash a} - \frac{4}{a} = \frac{a^{2} - 4}{a}\]

\[2)\frac{1}{x} + x^{\backslash x} - 2^{\backslash x} = \frac{1 + x^{2} - 2x}{x} =\]

\[= \frac{(x - 1)^{2}}{x}\]

\[3)\frac{m}{n^{3}} - \frac{1^{\backslash n^{2}}}{n} + m^{\backslash n^{3}} =\]

\[= \frac{m - n^{2} + mn^{3}}{n^{3}}\]

\[4)\frac{2k^{2}}{k - 5} - k^{\backslash k - 5} =\]

\[= \frac{2k^{2} - k \cdot (k - 5)}{k - 5} =\]

\[= \frac{2k^{2} - k^{2} + 5k}{k - 5} = \frac{k^{2} + 5k}{k - 5}\]

\[5)\ 3n^{\backslash 3n} - \frac{9n^{2} - 2}{3n} =\]

\[= \frac{3n \cdot 3n - 9n^{2} + 2}{3n} =\]

\[= \frac{9n^{2} - 9n^{2} + 2}{3n} = \frac{2}{3n}\]

\[6)\ 5^{\backslash y - 2} - \frac{4y - 12}{y - 2} =\]

\[= \frac{5 \cdot (y - 2) - 4y + 12}{y - 2} =\]

\[= \frac{5y - 10 - 4y + 12}{y - 2} = \frac{y + 2}{y - 2}\ \]