Сократите дробь:
а) $\frac{32a^4b - 80a^3b^2 + 50a^2b^3}{20ab^3 - 16a^2b^2}$;
б) $\frac{18a^3b^2 + 36ab^4}{96a^2b^5 + 96a^4b^3 + 24a^6b}$;
в) $\frac{18a^4b^2 - 30a^3b^3}{75a^2b^5 - 90a^3b^4 + 27a^4b^3}$;
г) $\frac{10a^2b^8 + 60a^4b^6 + 90a^6b^4}{45a^5b + 15a^3b^3}$.
$\frac{32a^4b - 80a^3b^2 + 50a^2b^3}{20ab^3 - 16a^2b^2} = \frac{2a^2b(16a^2 - 40ab + 25b^2)}{4ab^2(5b - 4a)} = \frac{a(4a - 5b)^2}{2b(5b - 4a)} = \frac{a(5b - 4a)^2}{2b(5b - 4a)} = \frac{a(5b - 4a)}{2b}$
$\frac{18a^3b^2 + 36ab^4}{96a^2b^5 + 96a^4b^3 + 24a^6b} = \frac{18ab^2(a^2 + 2b^2)}{24a^2b(4b^4 + 4a^2b + a^4)} = \frac{3b(a^2 + 2b^2)}{4a(2b^2 + a^2)^2} = \frac{3b}{4a(a^2 + 2b^2)}$
$\frac{18a^4b^2 - 30a^3b^3}{75a^2b^5 - 90a^3b^4 + 27a^4b^3} = \frac{6a^3b^2(3a - 5b)}{3a^2b^3(25b^2 - 30ab + 9a^2)^2} = \frac{2a(3a - 5b)}{b(5b - 3a)^2} = \frac{2a(3a - 5b)}{b(3a - 5b)^2} = \frac{2a}{b(3a - 5b)}$
$\frac{10a^2b^8 + 60a^4b^6 + 90a^6b^4}{45a^5b + 15a^3b^3} = \frac{10a^2b^4(b^4 + 6a^2b^2 + 9a^4)}{15a^3b(3a^2 + b^2)} = \frac{2b^3(b^2 + 3a^2)^2}{3a(3a^2 + b^2)} = \frac{2b^3(b^2 + 3a^2)}{3a}$
Пожауйста, оцените решение
