Сократите дробь:
1) $\frac{2m^2 - 72n^2}{(4m + 24n)^2}$;
2) $\frac{a^3 - 8}{ab - a - 2b + 2}$;
3) $\frac{a^3 + 2a^2b + ab^2}{a^3 - ab^2}$.
$\frac{2m^2 - 72n^2}{(4m + 24n)^2} = \frac{2(m^2 - 36n^2)}{16(m + 6n)^2} = \frac{2(m - 6n)(m + 6n)}{16(m + 6n)^2} = \frac{m - 6n}{8(m + 6n)}$
$\frac{a^3 - 8}{ab - a - 2b + 2} = \frac{(a - 2)(a^2 + 2a + 4)}{(ab - a) - (2b - 2)} = \frac{(a - 2)(a^2 + 2a + 4)}{a(b - 1) - 2(b - 1)} = \frac{(a - 2)(a^2 + 2a + 4)}{(b - 1)(a - 2)} = \frac{a^2 + 2a + 4}{b - 1}$
$\frac{a^3 + 2a^2b + ab^2}{a^3 - ab^2} = \frac{a(a^2 + 2ab + b^2)}{a(a^2 - b^2)} = \frac{a(a + b)^2}{a(a - b)(a + b)} = \frac{a + b}{a - b}$
Пожауйста, оцените решение
