Решите уравнение: (5x-2)/(x+2)=(6x-21)/(x-3).

\[\frac{5x - 2}{x + 2} = \frac{6x - 21}{x - 3}\]

\[ОДЗ:\ \ x + 2 \neq 0;x \neq - 2\]

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

\[\frac{5x - 2}{x + 2} - \frac{6x - 21}{x - 3} = 0\]

\[5x^{2} - 17x + 6 - 6x^{2} + 9x + 42 =\]

\[= 0\]

\[- x^{2} - 8x + 48 = 0\]

\[x^{2} + 8x - 48 = 0\]

\[x_{1} + x_{2} = - 8\]

\[x_{1} \cdot x_{2} = - 48 \Longrightarrow x_{1} = - 12;\ \ \]

\[x_{2} = 4\]

\[Ответ:x = - 12\ \ и\ \ x = 4.\]