Сократите дробь:
а) $\frac{15a^4b^2 - 15a^2}{45a^4b + 45a^3}$;
б) $\frac{18a^4b - 72a^2b}{48ab^2 - 24a^2b^2}$;
в) $\frac{17a^3b + 17a^4c}{51a^2b^2 - 51a^4c^2}$;
г) $\frac{36a^3b^2c - 36a^3b^3}{48ab^5 - 48ab^3c^2}$.
$\frac{15a^4b^2 - 15a^2}{45a^4b + 45a^3} = \frac{15a^2(a^2b^2 - 1)}{45a^3(ab + 1)} = \frac{(ab)^2 - 1}{3a(ab + 1)} = \frac{(ab - 1)(ab + 1)}{3a(ab + 1)} = \frac{ab - 1}{3a}$
$\frac{18a^4b - 72a^2b}{48ab^2 - 24a^2b^2} = \frac{18a^2b(a^2 - 4)}{24ab^2(2 - a)} = \frac{3a(a^2 - 2^2)}{4b(2 - a)} = -\frac{3a(a - 2)(a + 2)}{4b(a - 2)} = -\frac{3a(a + 2)}{4b}$
$\frac{17a^3b + 17a^4c}{51a^2b^2 - 51a^4c^2} = \frac{17a^3(b + ac)}{51a^2(b^2 - a^2c^2)} = \frac{a(b + ac)}{3(b - (ac)^2)} = \frac{a(b + ac)}{3(b - ac)(b + ac)} = \frac{a}{3(b - ac)}$
$\frac{36a^3b^2c - 36a^3b^3}{48ab^5 - 48ab^3c^2} = \frac{36a^3b^2(c - b)}{48ab^3(b^2 - c^2)} = \frac{3a^2(c - b)}{4b(b - c)(b + c)} = -\frac{3a^2(b - c)}{4b(b - c)(b + c)} = -\frac{3a^2}{4b(b + c)}$
Пожауйста, оцените решение
