Упростите выражение: 2/(x-4)-(x+8)/(x^2-16)-1/x.

Ответ:

\[\frac{2^{\backslash x(x + 4)}}{x - 4} - \frac{x + 8^{\backslash x}}{x^{2} - 16} - \frac{1^{\backslash x^{2} - 16}}{x} =\]

\[= \frac{2x^{2} + 8x - x^{2} - 8x - x^{2} + 16}{x\left( x^{2} - 16 \right)} =\]

\[= \frac{- x^{2} + 16}{x\left( x^{2} - 16 \right)} =\]

\[= - \frac{x^{2} - 16}{x\left( x^{2} - 16 \right)} = - \frac{1}{x}.\]