Решите уравнение 5/(x-3)-8/x=3

Ответ:

\[\ \frac{5}{x - 3} - \frac{8}{x} = 3\]

\[ОДЗ:x \neq 0\]

\[x - 3 \neq 0;x \neq 3\]

\[\frac{5x - 8 \cdot (x - 3)}{x(x - 3)} = 3\]

\[\frac{5x - 8x + 24}{x(x - 3)} = 3\]

\[- 3x + 24 = 3x^{2} - 9x\]

\[3x² - 6x - 24 = 0\ \ \ |\ :3\]

\[x^{2} - 2x - 8 = 0\]

\[D = b^{2} - 4ac = 4 - 4 \cdot ( - 8) =\]

\[= 4 + 32 = 36\ \]

\[x_{1} = \frac{2 - 6}{2} = - \frac{4}{2} = - 2\]

\[x_{2} = \frac{2 + 6}{2} = \frac{8}{2} = 4\]

\[Ответ:x = - 2\ \ и\ \ \ x = 4.\]