Найдите значение дроби:
а) $\frac{15a^2 - 10ab}{3ab - 2b^2}$ при a = −2, b = −0,1;
б) $\frac{9c^2 - 4d^2}{18c^2d - 12cd^2}$ при $c = \frac{2}{3}, d = \frac{1}{2}$;
в) $\frac{6x^2 + 12xy}{5xy + 10y^2}$ при $x = \frac{2}{3}, y = -0,4$;
г) $\frac{x^2 + 6xy + 9y^2}{4x^2 + 12xy}$ при x = −0,2, y = −0,6.
$\frac{15a^2 - 10ab}{3ab - 2b^2} = \frac{5a(3a - 2b)}{b(3a - 2b)} = \frac{5a}{b} = \frac{5 * (-2)}{-0,1} = 10 * 10 = 100$
$\frac{9c^2 - 4d^2}{18c^2d - 12cd^2} = \frac{(3c)^2 - (2d)^2}{6cd(3c - 2d)} = \frac{(3c - 2d)(3c + 2d)}{6cd(3c - 2d)} = \frac{3c + 2d}{6cd} = \frac{3 * \frac{2}{3} + 2 * \frac{1}{2}}{6 * \frac{2}{3} * \frac{1}{2}} = \frac{2 + 1}{1 * \frac{2}{1} * \frac{1}{1}} = \frac{3}{2} = 1,5$
$\frac{6x^2 + 12xy}{5xy + 10y^2} = \frac{6x(x + 2y)}{5y(x + 2y)} = \frac{6x}{5y} = \frac{6 * \frac{2}{3}}{5 * (-0,4)} = \frac{2 * \frac{2}{1}}{-2} = -\frac{4}{2} = -2$
$\frac{x^2 + 6xy + 9y^2}{4x^2 + 12xy} = \frac{(x + 3y)^2}{4x(x + 3y)} = \frac{x + 3y}{4x} = \frac{-0,2 + 3 * (-0,6)}{4 * (-0,2)} = \frac{-2}{-0,8} = 2 * \frac{10}{8} = \frac{10}{4} = \frac{5}{2} = 2,5$
Пожауйста, оцените решение
