Найдите значение дроби, предварительно сократив ее:
1) $\frac{15a^2 + 10ab}{3ab + 2b^2}$, если a = −2, b = 0,4;
2) $\frac{9b^2 - 4c^2}{12b^2c - 8bc^2}$, если $b = \frac{1}{3}$, c = −6;
3) $\frac{36x^2 - 12xy + y^2}{y^2 - 36x^2}$, если x = 1,2, y = −3;
4) $\frac{a^8 - a^6}{a^9 + a^8}$, если a = −0,1.
$\frac{15a^2 + 10ab}{3ab + 2b^2} = \frac{5a(3a + 2b)}{b(3a + 2b)} = \frac{5a}{b}$
при a = −2, b = 0,4:
$\frac{5 * (-2)}{0,4} = \frac{-10}{\frac{4}{10}} = -10 * \frac{10}{4} = -5 * 5 = -25$
$\frac{9b^2 - 4c^2}{12b^2c - 8bc^2} = \frac{(3b - 2c)(3b + 2c)}{4bc(3b - 2c)} = \frac{3b + 2c}{4bc}$
при $b = \frac{1}{3}$, c = −6:
$\frac{3 * \frac{1}{3} + 2 * (-6)}{4 * \frac{1}{3} * (-6)} = \frac{1 - 12}{4 * (-2)} = \frac{-11}{-8} = \frac{11}{8} = 1\frac{3}{8}$
$\frac{36x^2 - 12xy + y^2}{y^2 - 36x^2} = \frac{(6x - y)^2}{(y - 6x)(y + 6x)} = \frac{(y - 6x)^2}{(y - 6x)(y + 6x)} = \frac{y - 6x}{y + 6x}$
при x = 1,2, y = −3:
$\frac{-3 - 6 * 1,2}{-3 + 6 * 1,2} = \frac{-3 - 7,2}{-3 + 7,2} = \frac{-10,2}{4,2} = -\frac{102}{42} = -\frac{17}{7} = -2\frac{3}{7}$
$\frac{a^8 - a^6}{a^9 + a^8} = \frac{a^6(a^2 - 1)}{a^8(a + 1)} = \frac{a^6(a - 1)(a + 1)}{a^8(a + 1)} = \frac{a - 1}{a^2}$
при a = −0,1:
$\frac{-0,1 - 1}{(-0,1)^2} = \frac{-1,1}{0,01} = -110$
Пожауйста, оцените решение
