Question

$calculati\\x-3/x+1\geq 2x-5/x+2\\\\multumesc$

Answer 1

Explicație pas cu pas:

x + 1 ≠ 0 => x ≠ -1

x + 2 ≠ 0 => x ≠ -2

$\frac{x - 3}{x + 1} \geqslant \frac{2x - 5}{x + 2}$

$\frac{x - 3}{x + 1} - \frac{2x - 5}{x + 2} \geqslant 0$

$\frac{(x - 3)(x + 2) - (2x - 5)(x + 1)}{(x + 1)(x + 2)}\geqslant 0$

$\frac{{x}^{2} + 2x - 3x - 6 - 2 {x}^{2} + 5x - 2x + 5}{(x + 1)(x + 2)} \geqslant 0$

$\frac{ - {x}^{2} + 2x - 1}{(x + 1)(x + 2)} \geqslant 0$

$- \frac{{(x - 1)}^{2}}{(x + 1)(x + 2)} \geqslant 0$

$\frac{{(x - 1)}^{2}}{(x + 1)(x + 2)} \leqslant 0$

${(x - 1)}^{2} \geqslant 0 = > x = 1$

$\Rightarrow x\in \left( - 2 ; - 1\right)\ U \{1\}$