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(3x-2)/(2x+3)>(4x^2-3)/(1-x) desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
             2    
3*x - 2   4*x  - 3
------- > --------
2*x + 3    1 - x  
$$\frac{3 x - 2}{2 x + 3} > \frac{4 x^{2} - 3}{1 - x}$$
(3*x - 2)/(2*x + 3) > (4*x^2 - 3)/(1 - x)
Solución de la desigualdad en el gráfico
Respuesta rápida 2 [src]
        /   3       2              \                  /   3       2              \         /   3       2              \           
(CRootOf\8*x  + 15*x  - 11*x - 7, 0/, -3/2) U (CRootOf\8*x  + 15*x  - 11*x - 7, 1/, CRootOf\8*x  + 15*x  - 11*x - 7, 2/) U (1, oo)
$$x\ in\ \left(\operatorname{CRootOf} {\left(8 x^{3} + 15 x^{2} - 11 x - 7, 0\right)}, - \frac{3}{2}\right) \cup \left(\operatorname{CRootOf} {\left(8 x^{3} + 15 x^{2} - 11 x - 7, 1\right)}, \operatorname{CRootOf} {\left(8 x^{3} + 15 x^{2} - 11 x - 7, 2\right)}\right) \cup \left(1, \infty\right)$$
x in Union(Interval.open(1, oo), Interval.open(CRootOf(8*x^3 + 15*x^2 - 11*x - 7, 0), -3/2), Interval.open(CRootOf(8*x^3 + 15*x^2 - 11*x - 7, 1), CRootOf(8*x^3 + 15*x^2 - 11*x - 7, 2)))
Respuesta rápida [src]
  /                       /                 /   3       2              \    \     /           /   3       2              \         /   3       2              \    \\
Or\And(1 < x, x < oo), And\x < -3/2, CRootOf\8*x  + 15*x  - 11*x - 7, 0/ < x/, And\x < CRootOf\8*x  + 15*x  - 11*x - 7, 2/, CRootOf\8*x  + 15*x  - 11*x - 7, 1/ < x//
$$\left(1 < x \wedge x < \infty\right) \vee \left(x < - \frac{3}{2} \wedge \operatorname{CRootOf} {\left(8 x^{3} + 15 x^{2} - 11 x - 7, 0\right)} < x\right) \vee \left(x < \operatorname{CRootOf} {\left(8 x^{3} + 15 x^{2} - 11 x - 7, 2\right)} \wedge \operatorname{CRootOf} {\left(8 x^{3} + 15 x^{2} - 11 x - 7, 1\right)} < x\right)$$
((1 < x)∧(x < oo))∨((x < -3/2)∧(CRootOf(8*x^3 + 15*x^2 - 11*x - 7, 0) < x))∨((x < CRootOf(8*x^3 + 15*x^2 - 11*x - 7, 2))∧(CRootOf(8*x^3 + 15*x^2 - 11*x - 7, 1) < x))