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¿Cómo vas a descomponer esta atan((2*x+6)/2)+(2*x+5)/(20+12*x+2*x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
    /2*x + 6\       2*x + 5     
atan|-------| + ----------------
    \   2   /                  2
                20 + 12*x + 2*x 
2x+52x2+(12x+20)+atan(2x+62)\frac{2 x + 5}{2 x^{2} + \left(12 x + 20\right)} + \operatorname{atan}{\left(\frac{2 x + 6}{2} \right)}
atan((2*x + 6)/2) + (2*x + 5)/(20 + 12*x + 2*x^2)
Simplificación general [src]
5       /      2      \            
- + x + \10 + x  + 6*x/*atan(3 + x)
2                                  
-----------------------------------
                 2                 
           10 + x  + 6*x           
x+(x2+6x+10)atan(x+3)+52x2+6x+10\frac{x + \left(x^{2} + 6 x + 10\right) \operatorname{atan}{\left(x + 3 \right)} + \frac{5}{2}}{x^{2} + 6 x + 10}
(5/2 + x + (10 + x^2 + 6*x)*atan(3 + x))/(10 + x^2 + 6*x)
Unión de expresiones racionales [src]
            /      2      \            
5 + 2*x + 2*\10 + x  + 6*x/*atan(3 + x)
---------------------------------------
             /      2      \           
           2*\10 + x  + 6*x/           
2x+2(x2+6x+10)atan(x+3)+52(x2+6x+10)\frac{2 x + 2 \left(x^{2} + 6 x + 10\right) \operatorname{atan}{\left(x + 3 \right)} + 5}{2 \left(x^{2} + 6 x + 10\right)}
(5 + 2*x + 2*(10 + x^2 + 6*x)*atan(3 + x))/(2*(10 + x^2 + 6*x))
Respuesta numérica [src]
(5.0 + 2.0*x)/(20.0 + 2.0*x^2 + 12.0*x) + atan((2*x + 6)/2)
(5.0 + 2.0*x)/(20.0 + 2.0*x^2 + 12.0*x) + atan((2*x + 6)/2)
Potencias [src]
    5 + 2*x                   
---------------- + atan(3 + x)
        2                     
20 + 2*x  + 12*x              
2x+52x2+12x+20+atan(x+3)\frac{2 x + 5}{2 x^{2} + 12 x + 20} + \operatorname{atan}{\left(x + 3 \right)}
(5 + 2*x)/(20 + 2*x^2 + 12*x) + atan(3 + x)
Parte trigonométrica [src]
    5 + 2*x                   
---------------- + atan(3 + x)
        2                     
20 + 2*x  + 12*x              
2x+52x2+12x+20+atan(x+3)\frac{2 x + 5}{2 x^{2} + 12 x + 20} + \operatorname{atan}{\left(x + 3 \right)}
(5 + 2*x)/(20 + 2*x^2 + 12*x) + atan(3 + x)
Combinatoria [src]
                              2                               
5 + 2*x + 20*atan(3 + x) + 2*x *atan(3 + x) + 12*x*atan(3 + x)
--------------------------------------------------------------
                        /      2      \                       
                      2*\10 + x  + 6*x/                       
2x2atan(x+3)+12xatan(x+3)+2x+20atan(x+3)+52(x2+6x+10)\frac{2 x^{2} \operatorname{atan}{\left(x + 3 \right)} + 12 x \operatorname{atan}{\left(x + 3 \right)} + 2 x + 20 \operatorname{atan}{\left(x + 3 \right)} + 5}{2 \left(x^{2} + 6 x + 10\right)}
(5 + 2*x + 20*atan(3 + x) + 2*x^2*atan(3 + x) + 12*x*atan(3 + x))/(2*(10 + x^2 + 6*x))
Denominador racional [src]
                              2                               
5 + 2*x + 20*atan(3 + x) + 2*x *atan(3 + x) + 12*x*atan(3 + x)
--------------------------------------------------------------
                               2                              
                       20 + 2*x  + 12*x                       
2x2atan(x+3)+12xatan(x+3)+2x+20atan(x+3)+52x2+12x+20\frac{2 x^{2} \operatorname{atan}{\left(x + 3 \right)} + 12 x \operatorname{atan}{\left(x + 3 \right)} + 2 x + 20 \operatorname{atan}{\left(x + 3 \right)} + 5}{2 x^{2} + 12 x + 20}
(5 + 2*x + 20*atan(3 + x) + 2*x^2*atan(3 + x) + 12*x*atan(3 + x))/(20 + 2*x^2 + 12*x)
Compilar la expresión [src]
    5 + 2*x            /2*x + 6\
---------------- + atan|-------|
        2              \   2   /
20 + 2*x  + 12*x                
2x+52x2+12x+20+atan(2x+62)\frac{2 x + 5}{2 x^{2} + 12 x + 20} + \operatorname{atan}{\left(\frac{2 x + 6}{2} \right)}
(5 + 2*x)/(20 + 2*x^2 + 12*x) + atan((2*x + 6)/2)
Denominador común [src]
    5 + 2*x                   
---------------- + atan(3 + x)
        2                     
20 + 2*x  + 12*x              
2x+52x2+12x+20+atan(x+3)\frac{2 x + 5}{2 x^{2} + 12 x + 20} + \operatorname{atan}{\left(x + 3 \right)}
(5 + 2*x)/(20 + 2*x^2 + 12*x) + atan(3 + x)