Решите уравнение:9/(x+3)=2x-1.

Ответ:

\[\frac{9}{x + 3} = 2x - 1\]

\[ОДЗ:\ \ x + 3 \neq 0\]

\[\ \ \ \Longrightarrow x \neq - 3\]

\[9 = (2x - 1)(x + 3)\]

\[9 = 2x^{2} + 6x - x - 3\]

\[2x^{2} + 5x - 12 = 0\]

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

\[= 25 - 4 \cdot 2 \cdot ( - 12) =\]

\[= 25 + 96 = 121\]

\[x_{1} = \frac{- 5 + 11}{4} = \frac{6}{4} = 1,5\]

\[x_{2} = \frac{- 5 - 11}{4} = - \frac{16}{4} = - 4\]

\[Ответ:x = 1,5\ \ и\ \ x = - 4.\]