Решите уравнение 8/(x-3)-10/x=2

Ответ:

\[\frac{8}{x - 3} - \frac{10}{x} = 2\]

\[ОДЗ:\ \ x \neq 0\]

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

\[\frac{8x - 10 \cdot (x - 3)}{x(x - 3)} = 2\]

\[8x - 10x + 30 = 2x^{2} - 6x\]

\[2x^{2} - 6x + 2x - 30 = 0\]

\[2x² - 4x - 30 = 0\ \ \ |\ :2\]

\[x^{2} - 2x - 15 = 0\]

\[D = b^{2} - 4ac = 4 - 4 \cdot 1 \cdot ( - 15) =\]

\[= 4 + 60 = 64\]

\[x_{1} = \frac{2 + 8}{2} = \frac{10}{2} = 5\]

\[x_{2} = \frac{2 - 8}{2} = - \frac{6}{2} = - 3\]

\[Ответ:\ \ x = 5\ \ и\ \ \ x = - 3.\]