2. Сократите дробь: a) $$\frac{4mn(1-m)}{10n^2(m-1)^2}$$ б) $$\frac{a^3-3a^2b}{3a^3b-a^4b}$$ в) $$\frac{10m^2+20mn+10n^2}{25m^2-25n^2}$$

Решение:

а)

\(\frac{4mn(1-m)}{10n^2(m-1)^2} = \frac{4mn(-(m-1))}{10n^2(m-1)^2} = \frac{-4mn}{10n^2(m-1)} = \frac{-2m}{5n(m-1)}\)

б)

\(\frac{a^3-3a^2b}{3a^3b-a^4b} = \frac{a^2(a-3b)}{a^3b(3-a)} = \frac{a^2(a-3b)}{a^3b(-(a-3))} = \frac{a-3b}{-ab(a-3)} = \frac{3b-a}{ab(a-3)}\)

в)

\(\frac{10m^2+20mn+10n^2}{25m^2-25n^2} = \frac{10(m^2+2mn+n^2)}{25(m^2-n^2)} = \frac{10(m+n)^2}{25(m-n)(m+n)} = \frac{2(m+n)}{5(m-n)}\)

Ответ: а) $$\frac{-2m}{5n(m-1)}$$; б) $$\frac{3b-a}{ab(a-3)}$$; в) $$\frac{2(m+n)}{5(m-n)}$$