Решите уравнение: 14/(x^2-2x)-21/(x^2+2x)=5/x.

Ответ:

\[\frac{14}{x^{2} - 2x} - \frac{21}{x^{2} + 2x} = \frac{5}{x}\]

\[\frac{14}{x(x - 2)} - \frac{21}{x(x + 2)} - \frac{5}{x} = 0;\ \ \]

\[x \neq 0,\ x \neq 2,\ x \neq - 2\]

\[- 7x + 70 - 5x^{2} + 20 = 0\]

\[- 5x^{2} - 7x + 90 = 0\]

\[5x² + 7x - 90 = 0\]

\[x_{1} + x_{2} = - \frac{7}{5}\]

\[x_{1} \cdot x_{2} = - 18\]

\[\Longrightarrow x_{1} = 3,6;\ \ x_{2} = - 5\]

\[Ответ:x = 3,6;\ x = - 5.\]