$\frac{25a^2 - 36}{10a^2 - 9a + 2} : \frac{5a + 6}{5a - 2} + \frac{9a - 8}{1 - 2a}$
$10a^2 - 9a + 2 = 0$
$D = b^2 - 4ac = (-9)^2 - 4 * 10 * 2 = 81 - 80 = 1 > 0$
$a_1 = \frac{-b + \sqrt{D}}{2a} = \frac{9 + \sqrt{1}}{2 * 10} = \frac{9 + 1}{20} = \frac{10}{20} = 0,5$
$a_2 = \frac{-b - \sqrt{D}}{2a} = \frac{9 - \sqrt{1}}{2 * 10} = \frac{9 - 1}{20} = \frac{8}{20} = 0,4$
$10a^2 - 9a + 2 = 10(a - 0,5)(a - 0,4) = 2(a - 0,5) * 5(a - 0,4) = (2a - 1)(5a - 2)$
тогда:
$\frac{25a^2 - 36}{(2a - 1)(5a - 2)} : \frac{5a + 6}{5a - 2} + \frac{9a - 8}{1 - 2a} = \frac{(5a - 6)(5a + 6)}{(2a - 1)(5a - 2)} * \frac{5a - 2}{5a + 6} + \frac{9a - 8}{1 - 2a} = \frac{5a - 6}{2a - 1} + \frac{9a - 8}{1 - 2a} = \frac{5a - 6}{2a - 1} - \frac{9a - 8}{2a - 1} = \frac{5a - 6 - (9a - 8)}{2a - 1} = \frac{5a - 6 - 9a + 8}{2a - 1} = \frac{-4a + 2}{2a - 1} = \frac{-2(2a - 1)}{2a - 1} = -2$

$(\frac{2a}{a + 3} + \frac{1}{a - 1} - \frac{4}{a^2 + 2a - 3}) : \frac{2a + 1}{a + 3}$
$a^2 + 2a - 3 = 0$
$D = b^2 - 4ac = 2^2 - 4 * 1 * (-3) = 4 + 12 = 16 > 0$
$a_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-2 + \sqrt{16}}{2 * 1} = \frac{-2 + 4}{2} = \frac{2}{2} = 1$
$a_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-2 - \sqrt{16}}{2 * 1} = \frac{-2 - 4}{2} = \frac{-6}{2} = -3$
$a^2 + 2a - 3 = (a - 1)(a - (-3)) = (a - 1)(a + 3)$
тогда:
$(\frac{2a}{a + 3} + \frac{1}{a - 1} - \frac{4}{(a - 1)(a + 3)}) : \frac{2a + 1}{a + 3} = \frac{2a(a - 1) + a + 3 - 4}{(a - 1)(a + 3)} * \frac{a + 3}{2a + 1} = \frac{2a^2 - 2a + a - 1}{a - 1} * \frac{1}{2a + 1} = \frac{2a^2 - a - 1}{a - 1} * \frac{1}{2a + 1}$
$2a^2 - a - 1 = 0$
$D = b^2 - 4ac = (-1)^2 - 4 * 2 * (-1) = 1 + 8 = 9 > 0$
$a_1 = \frac{-b + \sqrt{D}}{2a} = \frac{1 + \sqrt{9}}{2 * 2} = \frac{1 + 3}{4} = \frac{4}{4} = 1$
$a_2 = \frac{-b - \sqrt{D}}{2a} = \frac{1 - \sqrt{9}}{2 * 2} = \frac{1 - 3}{4} = \frac{-2}{4} = -0,5$
$2a^2 - a - 1 = 2(a - 1)(a - (-0,5)) = 2(a - 1)(a + 0,5) = (a - 1)(2a + 1)$
тогда:
$\frac{(a - 1)(2a + 1)}{a - 1} * \frac{1}{2a + 1} = 1$