Решите неравенство: 4/(x-2)>=7/(x-3).

Ответ:

\[\frac{4}{x - 2} \geq \frac{7}{x - 3}\]

\[ОДЗ:\ \ x \neq 2;x \neq 3.\]

\[\frac{4 \cdot (x - 3) - 7(x - 2)}{(x - 2)(x - 3)} \geq 0\]

\[\frac{4x - 12 - 7x + 14}{(x - 2)(x - 3)} \geq 0\]

\[\frac{- 3x + 2}{(x - 2)(x - 3)} \geq 0\]

\[\frac{- 3\left( x - \frac{2}{3} \right)}{(x - 2)(x - 3)} \geq 0\]

\[x \leq \frac{2}{3};\ \ 2 < x < 3.\]

\[Ответ:x \leq \frac{2}{3};\ \ 2 < x < 3.\]