477 Сократите дробь при допустимых значениях переменных: a) \frac{5a + 5b}{a³+b³}; б) \frac{9c³ - 9d³}{5c - 5d}; в) \frac{25p² - 16q²}{125p³ - 64q³}; г) \frac{49m² - 16n²}{343m³ + 64n³}; д) \frac{1000x³ - 27y³}{64q³}; e) \frac{z⁴+ 12z²t+ 36t²}{z⁶ + 216t³}

a) $$\frac{5a + 5b}{a^3+b^3} = \frac{5(a+b)}{(a+b)(a^2-ab+b^2)} = \frac{5}{a^2-ab+b^2}$$ Ответ: $$\frac{5}{a^2-ab+b^2}$$ б) $$\frac{9c^3 - 9d^3}{5c - 5d} = \frac{9(c^3 - d^3)}{5(c - d)} = \frac{9(c-d)(c^2+cd+d^2)}{5(c-d)} = \frac{9(c^2+cd+d^2)}{5}$$ Ответ: $$\frac{9(c^2+cd+d^2)}{5}$$ в) $$\frac{25p^2 - 16q^2}{125p^3 - 64q^3} = \frac{(5p - 4q)(5p + 4q)}{(5p - 4q)(25p^2 + 20pq + 16q^2)} = \frac{5p + 4q}{25p^2 + 20pq + 16q^2}$$ Ответ: $$\frac{5p + 4q}{25p^2 + 20pq + 16q^2}$$ г) $$\frac{49m^2 - 16n^2}{343m^3 + 64n^3} = \frac{(7m - 4n)(7m + 4n)}{(7m + 4n)(49m^2 - 28mn + 16n^2)} = \frac{7m - 4n}{49m^2 - 28mn + 16n^2}$$ Ответ: $$\frac{7m - 4n}{49m^2 - 28mn + 16n^2}$$ д) $$\frac{1000x^3 - 27y^3}{64q^3} = \frac{(10x - 3y)(100x^2 + 30xy + 9y^2)}{64q^3}$$ Ответ: $$\frac{(10x - 3y)(100x^2 + 30xy + 9y^2)}{64q^3}$$ e) $$\frac{z^4+ 12z^2t+ 36t^2}{z^6 + 216t^3} = \frac{(z^2+6t)^2}{(z^2+6t)(z^4-6tz^2+36t^2)} = \frac{z^2+6t}{z^4-6tz^2+36t^2}$$ Ответ: $$\frac{z^2+6t}{z^4-6tz^2+36t^2}$$