Упростите выражение: (x^2-9)/(10-3x)*(2/(x-4)-4x/(x^2-x-12)-1/(x+3).

Ответ:

\[\frac{x^{2} - 9}{10 - 3x} \cdot \left( \frac{2}{x - 4} - \frac{4x}{x^{2} - x - 12} - \frac{1}{x + 3} \right) =\]

\[= \frac{x^{2} - 9}{10 - 3x} \cdot \left( \frac{2^{\backslash x + 3}}{x - 4} - \frac{4x}{(x - 4)(x + 3)} - \frac{1^{\backslash x - 4}}{x + 3} \right) =\]

\[= \frac{x^{2} - 9}{10 - 3x} \cdot \frac{2x + 6 - 4x - x + 4}{(x - 4)(x + 3)} =\]

\[= \frac{(x - 3)(x + 3)(10 - 3x)}{(10 - 3x)(x - 4)(x + 3)} =\]

\[= \frac{x - 3}{x - 4}.\]

\[x^{2} - x - 12 = (x + 3)(x - 4)\]

\[D = 1 + 48 = 49\]

\[x_{1} = \frac{1 + 7}{2} = 4;\]

\[x_{2} = \frac{1 - 7}{2} = - 3.\]