Упростите выражение:
1) $\frac{25 - 5a + 5b - ab}{25 + 5a - 5b - ab} * \frac{ab - 5a - 5b + 25}{ab + 5a + 5b + 25}$;
2) $\frac{a^2 - 2ab + b^2}{a^2 - ab - 4a + 4b} : \frac{a^2 - ab + 4a - 4b}{a^2 - 16}$.
$\frac{25 - 5a + 5b - ab}{25 + 5a - 5b - ab} * \frac{ab - 5a - 5b + 25}{ab + 5a + 5b + 25} = \frac{(25 - 5a) + (5b - ab)}{(25 + 5a) - (5b + ab)} * \frac{(ab - 5a) - (5b - 25)}{(ab + 5a) + (5b + 25)} = \frac{5(5 - a) + b(5 - a)}{5(5 + a) - b(5 + a)} * \frac{a(b - 5) - 5(b - 5)}{a(b + 5) + 5(b + 5)} = \frac{(5 - a)(5 + b)}{(5 + a)(5 - b)} * \frac{(b - 5)(a - 5)}{(b + 5)(a + 5)} = \frac{5 - a}{(5 + a)(5 - b)} * \frac{(b - 5)(a - 5)}{a + 5} = -\frac{5 - a}{(5 + a)(b - 5)} * \frac{(b - 5)(a - 5)}{a + 5} = -\frac{5 - a}{5 + a} * \frac{a - 5}{a + 5} = \frac{a - 5}{a + 5} * \frac{a - 5}{a + 5} = \frac{(a - 5)^2}{(a + 5)^2}$
$\frac{a^2 - 2ab + b^2}{a^2 - ab - 4a + 4b} : \frac{a^2 - ab + 4a - 4b}{a^2 - 16} = \frac{(a - b)^2}{(a^2 - ab) - (4a - 4b)} : \frac{(a^2 - ab) + (4a - 4b)}{(a - 4)(a + 4)} = \frac{(a - b)^2}{a(a - b) - 4(a - b)} : \frac{a(a - b) + 4(a - b)}{(a - 4)(a + 4)} = \frac{(a - b)^2}{(a - b)(a - 4)} : \frac{(a - b)(a + 4)}{(a - 4)(a + 4)} = \frac{a - b}{a - 4} : \frac{a - b}{a - 4} = \frac{a - b}{a - 4} * \frac{a - 4}{a - b} = \frac{1}{1} * \frac{1}{1} = 1$
Пожауйста, оцените решение
