Упростить выражение: 5/(x-7)-2/x-3x/(x^2-49)+21/(49-x^2).

Ответ:

\[\frac{5}{x - 7} - \frac{2}{x} - \frac{3x}{x^{2} - 49} + \frac{21}{49 - x^{2}} =\]

\[= \frac{5x^{2} + 35x - 2x^{2} + 98 - 3x^{2} - 21x}{x\left( x^{2} - 49 \right)} =\]

\[= \frac{14x - 98}{x\left( x^{2} - 49 \right)} =\]

\[= \frac{14(x - 7)}{x(x - 7)(x + 7)} = \frac{14}{x^{2} + 7x}.\]