Решите уравнение: 9/(x-2)-5/x=2.

Ответ:

\[\frac{9}{x - 2} - \frac{5}{x} = 2\ \ | \cdot x(x - 2)\]

\[ОДЗ:\]

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

\[9x - 5(x - 2) = 2x(x - 2)\]

\[9x - 5x + 10 = 2x^{2} - 4x\]

\[2x^{2} - 4x - 4x - 10 = 0\]

\[2x^{2} - 8x - 10 = 0\ \ |\ :2\]

\[x^{2} - 4x - 5 = 0\]

\[D_{1} = 4 + 5 = 9\]

\[x_{1} = 2 + 3 = 5;\]

\[x_{2} = 2 - 3 = - 1.\]

\[Ответ:x = - 1;x = 5.\]