Выполни умножение дробей.

1. a) $\frac{3a}{b} \cdot \frac{b}{6a} = \frac{3ab}{6ab} = \frac{1}{2}$ б) $\frac{-2x}{3y} \cdot \frac{y}{6x} = \frac{-2xy}{18xy} = -\frac{1}{9}$ в) $\frac{a^3-b^3}{12c} \cdot \frac{4c}{a^2+ab+b^2} = \frac{(a-b)(a^2+ab+b^2)}{12c} \cdot \frac{4c}{a^2+ab+b^2} = \frac{(a-b)4c}{12c} = \frac{a-b}{3}$ г) $\frac{18m^3}{5n^2} \cdot \frac{25n}{12m^2} = \frac{18 \cdot 25 m^3 n}{5 \cdot 12 m^2 n^2} = \frac{6 \cdot 5 m}{1 \cdot 2 n} = \frac{15m}{n}$ д) $6x \cdot \frac{a}{3x^2} = \frac{6xa}{3x^2} = \frac{2a}{x}$ е) $\frac{7y^3}{z^2} \cdot \frac{4x}{z^3} = \frac{28xy^3}{z^5}$ 2. a) $\frac{3}{x^2-2x} \cdot \frac{2x-4}{x} = \frac{3}{x(x-2)} \cdot \frac{2(x-2)}{x} = \frac{6(x-2)}{x^2(x-2)} = \frac{6}{x^2}$ б) $\frac{a-2b}{12c} \cdot \frac{18c^2}{2b-a} = \frac{-(2b-a)}{12c} \cdot \frac{18c^2}{2b-a} = -\frac{18c^2}{12c} = -\frac{3c}{2}$ в) $\frac{x^2-16}{8x^3} \cdot \frac{4x}{x+4} = \frac{(x-4)(x+4)4x}{8x^3(x+4)} = \frac{(x-4)4x}{8x^3} = \frac{x-4}{2x^2}$ г) $\frac{5-y}{2y} \cdot \frac{3y^2}{y^2-25} = \frac{-(y-5)3y^2}{2y(y-5)(y+5)} = -\frac{3y}{2(y+5)}$ д) $\frac{c^2+4c+4}{2c-6} \cdot \frac{5c+10}{c^2-9} = \frac{(c+2)^2}{2(c-3)} \cdot \frac{5(c+2)}{(c-3)(c+3)} = \frac{5(c+2)^3}{2(c-3)^2(c+3)}$ e) $\frac{3a-6b}{a+2} \cdot \frac{a^2-4}{a^2-4ab+4b^2} = \frac{3(a-2b)(a-2)(a+2)}{(a+2)(a-2b)^2} = \frac{3(a-2)}{a-2b}$ 3. a) $\frac{x^2-6x+9}{x^2-3x+9} \cdot \frac{x^3+27}{3x-9} = \frac{(x-3)^2(x+3)(x^2-3x+9)}{(x^2-3x+9)3(x-3)} = \frac{(x-3)(x+3)}{3} = \frac{x^2-9}{3}$ б) $\frac{x^2-ax+bx-ab}{x^2+ax-bx-ab} \cdot \frac{x^2+2ax+a^2}{x^2-2bx+b^2} = \frac{x(x-a)+b(x-a)}{x(x+a)-b(x+a)} \cdot \frac{(x+a)^2}{(x-b)^2} = \frac{(x-a)(x+b)(x+a)^2}{(x+a)(x-b)(x-b)^2} = \frac{(x-a)(x+a)}{(x-b)^2}$ 2. a) $\frac{5a^2+10ab+20b^2}{1} \cdot (a^2-8b^3) = (5a^2+10ab+20b^2)(a^2-8b^3)$ б) $(\frac{y^2}{-16x^2})^2 \cdot (\frac{-27y^3}{8x^2}) = \frac{y^4}{256x^4} \cdot (\frac{-27y^3}{8x^2}) = \frac{-27y^7}{2048x^6}$ в) $(\frac{c^3}{b})^3 \cdot (\frac{b^2}{c^4})^2 = \frac{c^9}{b^3} \cdot \frac{b^4}{c^8} = bc$ г) $\frac{a-b}{a+b} \cdot \frac{a^2+2ab+b^2}{a^2-2ab+b^2} = \frac{(a-b)(a+b)^2}{(a+b)(a-b)^2} = \frac{a+b}{a-b}$