Решите уравнение: 5/(x^2+3x)-15/(x^2-3x)=16/x.

Ответ:

\[\frac{5}{x^{2} + 3x} - \frac{15}{x^{2} - 3x} = \frac{16}{x}\]

\[8x² + 5x - 42 = 0\]

\[D = 25 + 1344 = 1369 = 37^{2}\]

\[x_{1} = \frac{- 5 + 37}{16} = 2;\ \ \ \]

\[x_{2} = \frac{- 5 - 37}{16} = - \frac{42}{16} =\]

\[= - \frac{21}{8} = - 2\frac{5}{8}.\]

\[Ответ:x = 2;\ x = - 2\frac{5}{8}.\]