Сократите дробь: 1) 4a/12b

13. Сократите дробь: 1) $\frac{4a}{12b} = \frac{a}{3b}$ 2) $\frac{8xy}{2xz} = \frac{4y}{z}$ 3) $\frac{10m^2}{15m^3} = \frac{2}{3m}$ 4) $\frac{3a^2bc}{18abc^3} = \frac{a}{6c^2}$ 5) $\frac{36m^3n^4}{24m^2n^6} = \frac{3m}{2n^2}$ 6) $\frac{39p^5q^8}{65p^8q^5} = \frac{3q^3}{5p^3}$ 14. Сократите дробь: 1) $\frac{4a+8b}{4a} = \frac{4(a+2b)}{4a} = \frac{a+2b}{a} = 1 + \frac{2b}{a}$ 2) $\frac{5x-10y}{3x-6y} = \frac{5(x-2y)}{3(x-2y)} = \frac{5}{3}$ 3) $\frac{x^2-25}{2x-10} = \frac{(x-5)(x+5)}{2(x-5)} = \frac{x+5}{2}$ 4) $\frac{6x^2-3x}{4-8x} = \frac{3x(2x-1)}{-4(2x-1)} = -\frac{3x}{4}$ 5) $\frac{m^2-16}{m^2+8m+16} = \frac{(m-4)(m+4)}{(m+4)^2} = \frac{m-4}{m+4}$ 6) $\frac{b^5-b^3}{b^2-b^4} = \frac{b^3(b^2-1)}{b^2(1-b^2)} = \frac{b^3(b^2-1)}{-b^2(b^2-1)} = -b$ 7) $\frac{a^3-27}{8a-24} = \frac{(a-3)(a^2+3a+9)}{8(a-3)} = \frac{a^2+3a+9}{8}$ 8) $\frac{6a^2+6a+6}{18a^3-18} = \frac{6(a^2+a+1)}{18(a^3-1)} = \frac{a^2+a+1}{3(a-1)(a^2+a+1)} = \frac{1}{3(a-1)}$ 9) $\frac{ax-ay-3x+3y}{9-a^2} = \frac{a(x-y)-3(x-y)}{(3-a)(3+a)} = \frac{(a-3)(x-y)}{-(a-3)(3+a)} = -\frac{x-y}{a+3} = \frac{y-x}{a+3}$ 15. Найдите значение выражения: 1) $\frac{a^8b^3+a^6b^5}{a^6b^3} = \frac{a^6b^3(a^2+b^2)}{a^6b^3} = a^2+b^2 = (0,3)^2 + (-0,4)^2 = 0,09 + 0,16 = 0,25$ 2) $\frac{7c^3-28c}{12c+12c^2+3c^3} = \frac{7c(c^2-4)}{3c(4+4c+c^2)} = \frac{7(c-2)(c+2)}{3(c+2)^2} = \frac{7(c-2)}{3(c+2)} = \frac{7(5-2)}{3(5+2)} = \frac{7 \cdot 3}{3 \cdot 7} = 1$ 3) $\frac{(2x-2y)^2}{2x^2-2y^2} = \frac{4(x-y)^2}{2(x-y)(x+y)} = \frac{2(x-y)}{x+y} = \frac{2(0,2 - (-0,4))}{0,2 + (-0,4)} = \frac{2(0,6)}{-0,2} = -6$ 4) $\frac{4x^2-40xy+100y^2}{15y-3x} = \frac{4(x^2-10xy+25y^2)}{-3(x-5y)} = \frac{4(x-5y)^2}{-3(x-5y)} = -\frac{4(x-5y)}{3} = -\frac{4(0,6)}{3} = -\frac{2,4}{3} = -0,8$ 16. Приведите дробь: 1) $\frac{a}{b^2} = \frac{a \cdot b^4}{b^2 \cdot b^4} = \frac{ab^4}{b^6}$ 2) $\frac{m}{3n} = \frac{m \cdot 5np}{3n \cdot 5np} = \frac{5mnp}{15n^2p}$ 3) $\frac{6}{7x^2y} = \frac{6 \cdot 4xy}{7x^2y \cdot 4xy} = \frac{24xy}{28x^3y^2}$ 4) $\frac{5}{a-3} = \frac{5 \cdot (-2)}{-(a-3) \cdot 2} = \frac{-10}{2a-6}$