Упростите выражение:
а) $(\frac{2m + 1}{2m - 1} - \frac{2m - 1}{2m + 1}) : \frac{4m}{10m - 5}$;
б) $\frac{x + 3}{x^2 + 9} * (\frac{x + 3}{x - 3} + \frac{x - 3}{x + 3})$.
$(\frac{2m + 1}{2m - 1} - \frac{2m - 1}{2m + 1}) : \frac{4m}{10m - 5} = \frac{(2m + 1)^2 - (2m - 1)^2}{(2m - 1)(2m + 1)} * \frac{5(2m - 1)}{4m} = \frac{4m^2 + 4m + 1 - (4m^2 - 4m + 1)}{2m + 1} * \frac{5}{4m} = \frac{4m^2 + 4m + 1 - 4m^2 + 4m - 1}{2m + 1} * \frac{5}{4m} = \frac{8m}{2m + 1} * \frac{5}{4m} = \frac{2}{2m + 1} * \frac{5}{1} = \frac{10}{2m + 1}$
$\frac{x + 3}{x^2 + 9} * (\frac{x + 3}{x - 3} + \frac{x - 3}{x + 3}) = \frac{x + 3}{x^2 + 9} * (\frac{(x + 3)^2 + (x - 3)^2}{(x - 3)(x + 3)}) = \frac{1}{x^2 + 9} * (\frac{x^2 + 6x + 9 + x^2 - 6x + 9}{x - 3}) = \frac{2(x^2 + 9)}{(x^2 + 9)(x - 3)} = \frac{2}{x - 3}$
Пожауйста, оцените решение
