31. Выполните деление: 1) 21b⁸ / 10c⁶ : 7b² / 30c³ ; 2) 40a⁵b⁹ / 39c⁶d¹⁴ : (-5a⁸b³ / 26c¹²d⁷) ; 3) 36x¹⁶y¹⁴ : 18x¹⁸y¹⁰ / 11m³ ; 4) 60m⁶n⁵ / 17p⁴ : (15m⁸n¹⁰); 5) 17a⁶b¹⁰ / 16c²d⁵ : 34a⁴b⁴ / 24c⁶d⁶ : 15b⁸d⁴ / 8a⁸c³ ; 6) (-9x⁵y² / 7z⁴)³ : (-9x⁴y¹⁰ / 7z³)⁴. 32. Выполните деление: 1) (x-3) / (6x³) : (x²-6x+9) / (18x⁴) ; 2) (x² + 4x) / (5x-5) : (7x + 28) / (x-1) ;

Выполним деление: 31. 1) $$\frac{21b^8}{10c^6} \div \frac{7b^2}{30c^3} = \frac{21b^8}{10c^6} \cdot \frac{30c^3}{7b^2} = \frac{21 \cdot 30 \cdot b^8 \cdot c^3}{10 \cdot 7 \cdot c^6 \cdot b^2} = \frac{3 \cdot 3 \cdot b^6}{c^3} = \frac{9b^6}{c^3}$$ 2) $$\frac{40a^5b^9}{39c^6d^{14}} \div \left(-\frac{5a^8b^3}{26c^{12}d^7}\right) = \frac{40a^5b^9}{39c^6d^{14}} \cdot \left(-\frac{26c^{12}d^7}{5a^8b^3}\right) = -\frac{40 \cdot 26 \cdot a^5 \cdot b^9 \cdot c^{12} \cdot d^7}{39 \cdot 5 \cdot c^6 \cdot d^{14} \cdot a^8 \cdot b^3} = -\frac{8 \cdot 2 \cdot b^6 \cdot c^6}{3 \cdot d^7 \cdot a^3} = -\frac{16b^6c^6}{3a^3d^7}$$ 3) $$36x^{16}y^{14} \div \frac{18x^{18}y^{10}}{11m^3} = 36x^{16}y^{14} \cdot \frac{11m^3}{18x^{18}y^{10}} = \frac{36 \cdot 11 \cdot x^{16} \cdot y^{14} \cdot m^3}{18 \cdot x^{18} \cdot y^{10}} = \frac{2 \cdot 11 \cdot y^4 \cdot m^3}{x^2} = \frac{22y^4m^3}{x^2}$$ 4) $$\frac{60m^6n^5}{17p^4} \div (15m^8n^{10}) = \frac{60m^6n^5}{17p^4} \cdot \frac{1}{15m^8n^{10}} = \frac{60 \cdot m^6 \cdot n^5}{17 \cdot p^4 \cdot 15 \cdot m^8 \cdot n^{10}} = \frac{4}{17p^4m^2n^5}$$ 5) $$\frac{17a^6b^{10}}{16c^2d^5} \div \frac{34a^4b^4}{24c^6d^6} \div \frac{15b^8d^4}{8a^8c^3} = \frac{17a^6b^{10}}{16c^2d^5} \cdot \frac{24c^6d^6}{34a^4b^4} \cdot \frac{8a^8c^3}{15b^8d^4} = \frac{17 \cdot 24 \cdot 8 \cdot a^6 \cdot a^4 \cdot a^8 \cdot b^{10} \cdot c^6 \cdot c^3 \cdot d^6}{16 \cdot 34 \cdot 15 \cdot c^2 \cdot d^5 \cdot b^4 \cdot b^8 \cdot d^4} = \frac{a^{10}c^7}{5b^2d^3}$$ 6) $$\left(-\frac{9x^5y^2}{7z^4}\right)^3 \div \left(-\frac{9x^4y^{10}}{7z^3}\right)^4 = \frac{\left(-\frac{9x^5y^2}{7z^4}\right)^3}{\left(-\frac{9x^4y^{10}}{7z^3}\right)^4} = \frac{-\frac{9^3x^{15}y^6}{7^3z^{12}}}{\frac{9^4x^{16}y^{40}}{7^4z^{12}}} = -\frac{9^3x^{15}y^6}{7^3z^{12}} \cdot \frac{7^4z^{12}}{9^4x^{16}y^{40}} = -\frac{7}{9xy^{34}}$$ 32. 1) $$\frac{x-3}{6x^3} \div \frac{x^2-6x+9}{18x^4} = \frac{x-3}{6x^3} \cdot \frac{18x^4}{x^2-6x+9} = \frac{x-3}{6x^3} \cdot \frac{18x^4}{(x-3)^2} = \frac{18x^4(x-3)}{6x^3(x-3)^2} = \frac{3x}{x-3}$$ 2) $$\frac{x^2+4x}{5x-5} \div \frac{7x+28}{x-1} = \frac{x(x+4)}{5(x-1)} \div \frac{7(x+4)}{x-1} = \frac{x(x+4)}{5(x-1)} \cdot \frac{x-1}{7(x+4)} = \frac{x(x+4)(x-1)}{5(x-1)7(x+4)} = \frac{x}{35}$$