\(\dfrac{-3}{x+2}< \dfrac{2}{3-x}\) Dk ( x ≠ -2 ; x ≠ 3)
MTC : (x + 2) (3 - x)
\(\Leftrightarrow\dfrac{-3\left(3-x\right)}{\left(x+2\right)\left(3-x\right)}< \dfrac{2\left(x+2\right)}{\left(x+2\right)\left(3-x\right)}\)
\(\Leftrightarrow\) -3(3 - x) < 2(x + 2)
\(\Leftrightarrow\) -9 + 3x < 2x + 4
\(\Leftrightarrow\) 3x - 2x < 4 + 9
\(\Leftrightarrow\) x < 13
Vay x < 13
Chuc ban hoc tot
Ta có: \(\dfrac{-3}{x+2}< \dfrac{2}{3-x}\)
\(\Leftrightarrow\dfrac{-3}{x+2}-\dfrac{2}{3-x}< 0\)
\(\Leftrightarrow\dfrac{-3}{x+2}+\dfrac{2}{x-3}< 0\)
\(\Leftrightarrow\dfrac{-3\left(x-3\right)+2\left(x+2\right)}{\left(x+2\right)\left(x-3\right)}< 0\)
\(\Leftrightarrow\dfrac{-3x+9+2x+4}{\left(x+2\right)\left(x-3\right)}< 0\)
\(\Leftrightarrow\dfrac{-x+13}{\left(x+2\right)\left(x-3\right)}< 0\)
\(\Leftrightarrow\left[{}\begin{matrix}x>13\\-2< x< 3\end{matrix}\right.\)
