Question

Calculati:
$\frac{x + 3}{2x + 1} \geqslant \frac{2x - 4}{x - 2}$
​

Answer 1

$\frac{x + 3}{2x + 1} \geqslant \frac{2x - 4}{x - 2} = > \frac{x + 3}{2x + 1} - \frac{2x - 4}{x - 2} \geqslant 0 = > \frac{x + 3}{2x + 1} - \frac{2(x - 2)}{x - 2} \geqslant 0 = > \frac{x + 3}{2x + 1} - 2 \geqslant 0 = > \frac{x + 3 - 2(2x + 1)}{2x + 1} \geqslant 0 = > = > \frac{x + 3 - 4x - 2}{2x + 1} \geqslant 0 = > \frac{ - 3x + 1}{2x + 1} \geqslant 0 = >$

{-3x+1

$\geqslant 0$

{2x+1>0 =>{x

$\leqslant \frac{1}{3}$

{x

$> - \frac{1}{2}$

{-3x+1

$\leqslant 0$

{2x+1<0 =>{x

$\geqslant \frac{1}{3}$

{x

$< - \frac{1}{2}$

=>x€(-1/2, 1/3].