Представьте в виде дроби: а) - 54a^6b^9 / c^12 * (- a^4c^20 / 12b^15); б) 42x^10y^6 / 55z^3t^5 : 18x^9y^8 / 77z^2t^6;

Давай решим примеры по алгебре, упростив выражения. a) $-\frac{54a^6b^9}{c^{12}} \cdot \left(-\frac{a^4c^{20}}{12b^{15}}\right) = \frac{54a^6b^9 \cdot a^4c^{20}}{12c^{12}b^{15}} = \frac{54}{12} \cdot a^{6+4} \cdot b^{9-15} \cdot c^{20-12} = 4,5 \cdot a^{10} \cdot b^{-6} \cdot c^8 = \frac{9a^{10}c^8}{2b^6}$ б) $\frac{42x^{10}y^6}{55z^3t^5} : \frac{18x^9y^8}{77z^2t^6} = \frac{42x^{10}y^6}{55z^3t^5} \cdot \frac{77z^2t^6}{18x^9y^8} = \frac{42 \cdot 77 \cdot x^{10-9} \cdot y^{6-8} \cdot z^{2-3} \cdot t^{6-5}}{55 \cdot 18} = \frac{3234 x \cdot y^{-2} \cdot z^{-1} \cdot t}{990} = \frac{49xt}{15y^2z}$ в) $\frac{98m^8n^{14}}{p^{17}} : (49m^5n^{14}p^2) = \frac{98m^8n^{14}}{p^{17} \cdot 49m^5n^{14}p^2} = \frac{98}{49} \cdot m^{8-5} \cdot n^{14-14} \cdot p^{-17-2} = 2m^3p^{-19} = \frac{2m^3}{p^{19}}$ г) $\frac{cd}{d^2-c^2} \cdot \left(\frac{d-9}{d} - \frac{c-9}{c}\right) = \frac{cd}{(d-c)(d+c)} \cdot \left(\frac{c(d-9) - d(c-9)}{dc}\right) = \frac{cd}{(d-c)(d+c)} \cdot \frac{cd-9c-cd+9d}{dc} = \frac{cd}{(d-c)(d+c)} \cdot \frac{9d-9c}{dc} = \frac{cd \cdot 9(d-c)}{(d-c)(d+c)dc} = \frac{9}{d+c}$ д) $\frac{3-x}{x^3} \cdot \frac{xy-x}{3-x} + \frac{3-y}{3x^2} = \frac{3-x}{x^3} \cdot \frac{x(y-1)}{3-x} + \frac{3-y}{3x^2} = \frac{x(y-1)}{x^3} + \frac{3-y}{3x^2} = \frac{y-1}{x^2} + \frac{3-y}{3x^2} = \frac{3(y-1) + 3-y}{3x^2} = \frac{3y-3+3-y}{3x^2} = \frac{2y}{3x^2}$ е) $\frac{5a+5b}{b} \cdot \frac{6b^2}{a^2-b^2} = \frac{5(a+b)}{b} \cdot \frac{6b^2}{(a-b)(a+b)} = \frac{5 \cdot 6b}{a-b} = \frac{30b}{a-b}$