Решите уравнение: (5x-7)/(x-3)=(4x-3)/x.

Ответ:

\[\frac{5x - 7}{x - 3} = \frac{4x - 3}{x}\]

\[ОДЗ:\ \ x \neq 0\]

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

\[\frac{5x - 7}{x - 3} - \frac{4x - 3}{x} = 0\]

\[\frac{x(5x - 7) - (x - 3)(4x - 3)}{x(x - 3)} =\]

\[= 0\]

\[x^{2} + 8x - 9 = 0\]

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

\[x_{1} \cdot x_{2} = - 9 \Longrightarrow x_{1} = - 9;\ \ x_{2} = 1\]

\[Ответ:x = - 9\ \ и\ \ x = 1.\]