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(x^2-6*x+8)/(x+1)-(x+4)/(x^2+3*x+2)>=0

(x^2-6*x+8)/(x+1)-(x+4)/(x^2+3*x+2)>=0 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
 2                              
x  - 6*x + 8      x + 4         
------------ - ------------ >= 0
   x + 1        2               
               x  + 3*x + 2     
$$- \frac{x + 4}{\left(x^{2} + 3 x\right) + 2} + \frac{\left(x^{2} - 6 x\right) + 8}{x + 1} \geq 0$$
-(x + 4)/(x^2 + 3*x + 2) + (x^2 - 6*x + 8)/(x + 1) >= 0
Solución de la desigualdad en el gráfico
Respuesta rápida [src]
  /   /            / 3      2              \        \     /            / 3      2              \        \     /       / 3      2              \             \\
Or\And\x <= CRootOf\x  - 4*x  - 5*x + 12, 0/, -2 < x/, And\x <= CRootOf\x  - 4*x  - 5*x + 12, 1/, -1 < x/, And\CRootOf\x  - 4*x  - 5*x + 12, 2/ <= x, x < oo//
$$\left(x \leq \operatorname{CRootOf} {\left(x^{3} - 4 x^{2} - 5 x + 12, 0\right)} \wedge -2 < x\right) \vee \left(x \leq \operatorname{CRootOf} {\left(x^{3} - 4 x^{2} - 5 x + 12, 1\right)} \wedge -1 < x\right) \vee \left(\operatorname{CRootOf} {\left(x^{3} - 4 x^{2} - 5 x + 12, 2\right)} \leq x \wedge x < \infty\right)$$
((-2 < x)∧(x <= CRootOf(x^3 - 4*x^2 - 5*x + 12, 0)))∨((-1 < x)∧(x <= CRootOf(x^3 - 4*x^2 - 5*x + 12, 1)))∨((x < oo)∧(CRootOf(x^3 - 4*x^2 - 5*x + 12, 2) <= x))
Respuesta rápida 2 [src]
            / 3      2              \                / 3      2              \            / 3      2              \     
(-2, CRootOf\x  - 4*x  - 5*x + 12, 0/] U (-1, CRootOf\x  - 4*x  - 5*x + 12, 1/] U [CRootOf\x  - 4*x  - 5*x + 12, 2/, oo)
$$x\ in\ \left(-2, \operatorname{CRootOf} {\left(x^{3} - 4 x^{2} - 5 x + 12, 0\right)}\right] \cup \left(-1, \operatorname{CRootOf} {\left(x^{3} - 4 x^{2} - 5 x + 12, 1\right)}\right] \cup \left[\operatorname{CRootOf} {\left(x^{3} - 4 x^{2} - 5 x + 12, 2\right)}, \infty\right)$$
x in Union(Interval.Lopen(-2, CRootOf(x^3 - 4*x^2 - 5*x + 12, 0)), Interval.Lopen(-1, CRootOf(x^3 - 4*x^2 - 5*x + 12, 1)), Interval(CRootOf(x^3 - 4*x^2 - 5*x + 12, 2), oo))
Gráfico
(x^2-6*x+8)/(x+1)-(x+4)/(x^2+3*x+2)>=0 desigualdades