Решите уравнение: 3/(x-5)+8/x=2.

Ответ:

\[\frac{3^{\backslash x}}{x - 5} + \frac{8^{\backslash x - 5}}{x} = 2^{\backslash x(x - 5)}\]

\[\frac{3x + 8x - 40 - 2x^{2} + 10x}{x(x - 5)} = 0\]

\[ОДЗ:x \neq 0;x \neq 5.\]

\[- 2x^{2} + 21x - 40 = 0\]

\[2x^{2} - 21x + 40 = 0\]

\[D = 441 - 320 = 121\]

\[x_{1} = \frac{21 + 11}{4} = 8;\]

\[x_{2} = \frac{21 - 11}{4} = \frac{10}{4} = 2,5.\]

\[Ответ:x = 2,5;x = 8.\]