Выполните действия: a) $$\frac{5}{x-2} - \frac{4x-7}{x-2}$$ б) $$\frac{5}{8x^5} - \frac{3}{6x^3}$$ в) $$\frac{54x^2y^5}{25a^4b^2} \cdot (-\frac{70a^7b^6}{63x^3y^3})$$ г) $$\frac{x^2 + 5x}{12x^6} : \frac{x^2-25}{6x^{12}}$$ д) $$\left(-\frac{3m^5}{5n^2}\right)^3$$

a) $$\frac{5}{x-2} - \frac{4x-7}{x-2} = \frac{5 - (4x - 7)}{x - 2} = \frac{5 - 4x + 7}{x - 2} = \frac{12 - 4x}{x - 2} = \frac{-4(x - 3)}{x - 2}$$ б) $$\frac{5}{8x^5} - \frac{3}{6x^3} = \frac{5}{8x^5} - \frac{1}{2x^3} = \frac{5}{8x^5} - \frac{4x^2}{8x^5} = \frac{5 - 4x^2}{8x^5}$$ в) $$\frac{54x^2y^5}{25a^4b^2} \cdot (-\frac{70a^7b^6}{63x^3y^3}) = -\frac{54 \cdot 70 x^2y^5 a^7b^6}{25 \cdot 63 a^4b^2 x^3y^3} = -\frac{6 \cdot 14 a^3 b^4 y^2}{5 \cdot 9 x} = -\frac{84 a^3 b^4 y^2}{45 x} = -\frac{28a^3b^4y^2}{15x}$$ г) $$\frac{x^2 + 5x}{12x^6} : \frac{x^2 - 25}{6x^{12}} = \frac{x(x + 5)}{12x^6} \cdot \frac{6x^{12}}{(x - 5)(x + 5)} = \frac{6x^{13}(x+5)}{12x^6(x-5)(x+5)} = \frac{x^7}{2(x-5)}$$ д) $$\left(-\frac{3m^5}{5n^2}\right)^3 = -\frac{(3m^5)^3}{(5n^2)^3} = -\frac{27m^{15}}{125n^6}$$