Решите уравнение 3/(x-5)+8/x=2

Ответ:

\[\ \frac{3}{x - 5} + \frac{8}{x} = 2\]

\[\frac{3x + 8 \cdot (x - 5)}{x(x - 5)} = 2;\ \ \ \ \ x \neq 0;\ \ x \neq 5\]

\[3x + 8x - 40 = 2x^{2} - 10x\]

\[2x^{2} - 10x - 11x + 40 = 0\]

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

\[D = b^{2} - 4ac = 441 - 4 \cdot 2 \cdot 40 = 441 -\]

\[- 320 = 121\]

\[x_{1} = \frac{21 + 11}{4} = \frac{32}{4} = 8\]

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

\[Ответ:x = 8\ \ \ и\ \ \ x = 2,5.\]