4. Сократите дробь: a) \(\frac{a^4 - b^2}{a^2 + b}\) б) \(\frac{4c^6 - 25d^8}{-2c^3 - 5d^4}\) в) \(\frac{a^3 + b^3}{a^2 - ab + b^2}\) г) \(\frac{c - 2}{c^3 - 8}\)

Решение:

1. \(\frac{a^4 - b^2}{a^2 + b} = \frac{(a^2 - b)(a^2 + b)}{a^2 + b} = a^2 - b\)
2. \(\frac{4c^6 - 25d^8}{-2c^3 - 5d^4} = \frac{(2c^3 - 5d^4)(2c^3 + 5d^4)}{-(2c^3 + 5d^4)} = -(2c^3 - 5d^4) = 5d^4 - 2c^3\)
3. \(\frac{a^3 + b^3}{a^2 - ab + b^2} = \frac{(a + b)(a^2 - ab + b^2)}{a^2 - ab + b^2} = a + b\)
4. \(\frac{c - 2}{c^3 - 8} = \frac{c - 2}{(c - 2)(c^2 + 2c + 4)} = \frac{1}{c^2 + 2c + 4}\)

Ответ: а) \(a^2 - b\), б) \(5d^4 - 2c^3\), в) \(a + b\), г) \(\frac{1}{c^2 + 2c + 4}\).