[tex] \frac{x + 3}{2x + 1} \geqslant \frac{2x - 4}{x - 2} = > \frac{x + 3}{2x + 1} - \frac{2x - 4}{x - 2} \geqslant 0 = > \frac{x + 3}{2x + 1} - \frac{2(x - 2)}{x - 2} \geqslant 0 = > \frac{x + 3}{2x + 1} - 2 \geqslant 0 = > \frac{x + 3 - 2(2x + 1)}{2x + 1} \geqslant 0 = > = > \frac{x + 3 - 4x - 2}{2x + 1} \geqslant 0 = > \frac{ - 3x + 1}{2x + 1} \geqslant 0 = > [/tex]
{-3x+1
[tex] \geqslant 0[/tex]
{2x+1>0 =>{x
[tex] \leqslant \frac{1}{3} [/tex]
{x
[tex] > - \frac{1}{2} [/tex]
{-3x+1
[tex] \leqslant 0[/tex]
{2x+1<0 =>{x
[tex] \geqslant \frac{1}{3} [/tex]
{x
[tex] < - \frac{1}{2} [/tex]
=>x€(-1/2, 1/3].
