$\frac{3m^2 + 6mn + 3n^2}{6n^2 - 6m^2} = \frac{3(m^2 + 2mn + n^2)}{6(n^2 - m^2)} = \frac{(m + n)^2}{2(n - m)(n + m)} = \frac{m + n}{2(n - m)}$
при m = 0,5, $n = \frac{2}{3}$:
$\frac{0,5 + \frac{2}{3}}{2(\frac{2}{3} - 0,5)} = \frac{\frac{1}{2} + \frac{2}{3}}{2(\frac{2}{3} - \frac{1}{2})} = \frac{\frac{3}{6} + \frac{4}{6}}{2(\frac{4}{6} - \frac{3}{6})} = \frac{\frac{7}{6}}{2 * \frac{1}{6}} = \frac{7}{6} * 3 = \frac{7}{2} = 3,5$

$\frac{2c^2 - 2b^2}{4b^2 - 8bc + 4c^2} = \frac{2(c^2 - b^2)}{4(b^2 - 2bc + c^2)} = \frac{(c - b)(c + b)}{2(b - c)^2} = \frac{(c - b)(c + b)}{2(c - b)^2} = \frac{c + b}{2(c - b)}$
при b = 0,25, $c = \frac{1}{3}$:
$\frac{\frac{1}{3} + 0,25}{2(\frac{1}{3} - 0,25)} = \frac{\frac{1}{3} + \frac{1}{4}}{2(\frac{1}{3} - \frac{1}{4})} = \frac{\frac{4}{12} + \frac{3}{12}}{2(\frac{4}{12} - \frac{3}{12})} = \frac{\frac{7}{12}}{2 * \frac{1}{12}} = \frac{\frac{7}{12}}{\frac{1}{6}} = \frac{7}{12} * 6 = \frac{7}{2} = 3,5$

$\frac{4xy}{y^2 - x^2} : (\frac{1}{y^2 - x^2} + \frac{1}{x^2 + 2xy + y^2}) = \frac{4xy}{(y - x)(y + x)} : (\frac{1}{(y - x)(y + x)} + \frac{1}{(x + y)^2}) = \frac{4xy}{(y - x)(y + x)} : \frac{x + y + y - x}{(y - x)(y + x)^2} = \frac{4xy}{(y - x)(y + x)} : \frac{2y}{(y - x)(y + x)^2} = \frac{4xy}{(y - x)(y + x)} * \frac{(y - x)(y + x)^2}{2y} = \frac{2x}{1} * \frac{y + x}{1} = 2x(y + x)$
при x = 0,35, y = 7,65:
2 * 0,35 * (7,65 + 0,35) = 0,7 * 8 = 5,6

$\frac{x^2 + 25}{(x - 5)^3} + \frac{10x}{(5 - x)^3} = \frac{x^2 + 25}{(x - 5)^3} - \frac{10x}{(x - 5)^3} = \frac{x^2 + 25 - 10x}{(x - 5)^3} = \frac{(x - 5)^2}{(x - 5)^3} = \frac{1}{x - 5}$
при x = 5,125:
$\frac{1}{5,125 - 5} = \frac{1}{0,125} = \frac{1000}{125} = 8$