Упростите выражение:
1) $\frac{\frac{a - b}{a + b} + \frac{b}{a}}{\frac{a}{a + b} - \frac{a - b}{a}}$;
2) $\frac{1}{1 - \frac{1}{1 - \frac{1}{a + 1}}}$.
$\frac{\frac{a - b}{a + b} + \frac{b}{a}}{\frac{a}{a + b} - \frac{a - b}{a}} = \frac{\frac{a(a - b) + b(a + b)}{a(a + b)}}{\frac{a^2 - (a - b)(a + b)}{a(a + b)}} = \frac{a^2 - ab + ab + b^2}{a^2 - (a^2 - b^2)} = \frac{a^2 + b^2}{a^2 - a^2 + b^2} = \frac{a^2 + b^2}{b^2}$
$\frac{1}{1 - \frac{1}{1 - \frac{1}{a + 1}}} = \frac{1}{1 - \frac{1}{\frac{a + 1 - 1}{a + 1}}} = \frac{1}{1 - \frac{1}{\frac{a}{a + 1}}} = \frac{1}{1 - \frac{a + 1}{a}} = \frac{1}{\frac{a - (a + 1)}{a}} = \frac{1}{\frac{a - a - 1}{a}} = \frac{1}{\frac{-1}{a}} = \frac{a}{-1} = -a$
Пожауйста, оцените решение
