Упростите выражение:
1) $\frac{a + \frac{25}{a + 10}}{\frac{25}{a} - a}$;
2) $1 - \frac{1}{1 - \frac{a}{1 - \frac{1}{a + 1}}}$.
$\frac{a + \frac{25}{a + 10}}{\frac{25}{a} - a} = \frac{\frac{a(a + 10) + 25}{a + 10}}{\frac{25 - a^2}{a}} = \frac{\frac{a^2 + 10a + 25}{a + 10}}{\frac{(5 - a)(5 + a)}{a}} = \frac{(a + 5)^2}{a + 10} * \frac{a}{(5 - a)(5 + a)} = \frac{a(a + 5)}{(a + 10)(5 - a)}$
$1 - \frac{1}{1 - \frac{a}{1 - \frac{1}{a + 1}}} = 1 - \frac{1}{1 - \frac{a}{\frac{a + 1 - 1}{a + 1}}} = 1 - \frac{1}{1 - \frac{a}{\frac{a}{a + 1}}} = 1 - \frac{1}{1 - \frac{a(a + 1)}{a}} = 1 - \frac{1}{1 - (a + 1)} = 1 - \frac{1}{1 - a - 1} = 1 + \frac{1}{a} = \frac{a + 1}{a}$
Пожауйста, оцените решение
