(3*x^2-10x^2+10x-5)/(3x^2-10x+3)

+ desigualdades

¡Resolver la desigualdad!

En la desigualdad la incógnita

Solución

Ha introducido [src]

   2       2                                 
3*x  - 10*x  + 10*x - 5         1        1   
----------------------- < x + ----- + -------
       2                      x - 2   3*x - 1
    3*x  - 10*x + 3                          

$$\frac{\left(10 x + \left(- 10 x^{2} + 3 x^{2}\right)\right) - 5}{\left(3 x^{2} - 10 x\right) + 3} < \left(x + \frac{1}{x - 2}\right) + \frac{1}{3 x - 1}$$

(10*x - 10*x^2 + 3*x^2 - 5)/(3*x^2 - 10*x + 3) < x + 1/(x - 2) + 1/(3*x - 1)

Solución de la desigualdad en el gráfico

Respuesta rápida 2 [src]

        /   3      2             \         /   3      2             \                          /   3      2             \           
(CRootOf\3*x  - 6*x  - 3*x + 1, 0/, CRootOf\3*x  - 6*x  - 3*x + 1, 1/) U (1/3, 1) U (2, CRootOf\3*x  - 6*x  - 3*x + 1, 2/) U (3, oo)

$$x\ in\ \left(\operatorname{CRootOf} {\left(3 x^{3} - 6 x^{2} - 3 x + 1, 0\right)}, \operatorname{CRootOf} {\left(3 x^{3} - 6 x^{2} - 3 x + 1, 1\right)}\right) \cup \left(\frac{1}{3}, 1\right) \cup \left(2, \operatorname{CRootOf} {\left(3 x^{3} - 6 x^{2} - 3 x + 1, 2\right)}\right) \cup \left(3, \infty\right)$$

x in Union(Interval.open(1/3, 1), Interval.open(2, CRootOf(3*x^3 - 6*x^2 - 3*x + 1, 2)), Interval.open(3, oo), Interval.open(CRootOf(3*x^3 - 6*x^2 - 3*x + 1, 0), CRootOf(3*x^3 - 6*x^2 - 3*x + 1, 1)))

Respuesta rápida [src]

  /                        /                  /   3      2             \\                         /           /   3      2             \         /   3      2             \    \\
Or\And(1/3 < x, x < 1), And\2 < x, x < CRootOf\3*x  - 6*x  - 3*x + 1, 2//, And(3 < x, x < oo), And\x < CRootOf\3*x  - 6*x  - 3*x + 1, 1/, CRootOf\3*x  - 6*x  - 3*x + 1, 0/ < x//

$$\left(\frac{1}{3} < x \wedge x < 1\right) \vee \left(2 < x \wedge x < \operatorname{CRootOf} {\left(3 x^{3} - 6 x^{2} - 3 x + 1, 2\right)}\right) \vee \left(3 < x \wedge x < \infty\right) \vee \left(x < \operatorname{CRootOf} {\left(3 x^{3} - 6 x^{2} - 3 x + 1, 1\right)} \wedge \operatorname{CRootOf} {\left(3 x^{3} - 6 x^{2} - 3 x + 1, 0\right)} < x\right)$$

((1/3 < x)∧(x < 1))∨((3 < x)∧(x < oo))∨((2 < x)∧(x < CRootOf(3*x^3 - 6*x^2 - 3*x + 1, 2)))∨((x < CRootOf(3*x^3 - 6*x^2 - 3*x + 1, 1))∧(CRootOf(3*x^3 - 6*x^2 - 3*x + 1, 0) < x))