$\frac{3x^{-2} + 2y^{-2}}{2x^{-2} + 3y^{-2}} = \frac{\frac{3}{x^2} + \frac{2}{y^2}}{\frac{2}{x^2} + \frac{3}{y^2}} = \frac{\frac{3y^2 + 2x^2}{x^2y^2}}{\frac{2y^2 + 3x^2}{x^2y^2}} = \frac{3y^2 + 2x^2}{x^2y^2} * \frac{x^2y^2}{2y^2 + 3x^2} = \frac{3y^2 + 2x^2}{2y^2 + 3x^2}$
при $\frac{x}{y} = 2^{-1} = \frac{1}{2}$:
y = 2x, тогда:
$\frac{3y^2 + 2x^2}{2y^2 + 3x^2} = \frac{3 * (2x)^2 + 2x^2}{2 * (2x)^2 + 3x^2} = \frac{12x^2 + 2x^2}{8x^2 + 3x^2} = \frac{14x^2}{11x^2} = \frac{14}{11} = 1\frac{3}{11}$

$\frac{3x^{-2} - 2y^{-2}}{2x^{-2} - 3y^{-2}} = \frac{\frac{3}{x^2} - \frac{2}{y^2}}{\frac{2}{x^2} - \frac{3}{y^2}} = \frac{\frac{3y^2 - 2x^2}{x^2y^2}}{\frac{2y^2 - 3x^2}{x^2y^2}} = \frac{3y^2 - 2x^2}{x^2y^2} * \frac{x^2y^2}{2y^2 - 3x^2} = \frac{3y^2 - 2x^2}{2y^2 - 3x^2}$
при $\frac{x}{y} = 3^{-1} = \frac{1}{3}$:
y = 3x, тогда:
$\frac{3y^2 - 2x^2}{2y^2 - 3x^2} = \frac{3 * (3x)^2 - 2x^2}{2 * (3x)^2 - 3x^2} = \frac{25x^2}{15x^2} = \frac{25}{15} = \frac{5}{3} = 1\frac{2}{3}$