Решите уравнение 6/(x-2)+5/x=3

Ответ:

\[\ \frac{6}{x - 2} + \frac{5}{x} = 3\]

\[\frac{6x + 5 \cdot (x - 2)}{x(x - 2)} = 3\ \ \ \ \ \ \ | \cdot x(x - 2);\ \ \ \ \]

\[x \neq 0;\ \ x \neq 2.\]

\[6x + 5x - 10 = 3x^{2} - 6x\]

\[3x^{2} - 6x - 6x - 5x + 10 = 0\]

\[3x^{2} - 17x + 10 = 0\]

\[D = b^{2} - 4ac = 289 - 4 \cdot 3 \cdot 10 =\]

\[= 289 - 120 = 169\]

\[x_{1} = \frac{17 + 13}{6} = \frac{30}{6} = 5\]

\[x_{2} = \frac{17 - 13}{6} = \frac{4}{6} = \frac{2}{3}\]

\[Ответ:\ \ x_{1} = 5\ \ \ и\ \ x_{2} = \frac{2}{3}.\]