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Simplificación de expresiones/ Descomposición en fracciones simples/ log((p+(a-4*p)/6)*a/(((a-2*p)*p)))/((k*(a+2*p)^2))+(a-4*p)/(3*((k*a*(a+2*p)*(a-(a-4*p)/3))))

¿Cómo vas a descomponer esta log((p+(a-4*p)/6)*a/(((a-2*p)*p)))/((k*(a+2*p)^2))+(a-4*p)/(3*((k*a*(a+2*p)*(a-(a-4*p)/3)))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   //    a - 4*p\  \                                
   ||p + -------|*a|                                
   |\       6   /  |                                
log|---------------|                                
   \  (a - 2*p)*p  /              a - 4*p           
-------------------- + -----------------------------
               2                       /    a - 4*p\
    k*(a + 2*p)        3*k*a*(a + 2*p)*|a - -------|
                                       \       3   /
a−4p3ak(a+2p)(a−a−4p3)+log⁡(a(p+a−4p6)p(a−2p))k(a+2p)2\frac{a - 4 p}{3 a k \left(a + 2 p\right) \left(a - \frac{a - 4 p}{3}\right)} + \frac{\log{\left(\frac{a \left(p + \frac{a - 4 p}{6}\right)}{p \left(a - 2 p\right)} \right)}}{k \left(a + 2 p\right)^{2}} 
log(((p + (a - 4*p)/6)*a)/(((a - 2*p)*p)))/((k*(a + 2*p)^2)) + (a - 4*p)/((3*(((k*a)*(a + 2*p))*(a - (a - 4*p)/3))))
Simplificación general [src] 
a              / a*(a + 2*p) \
- - 2*p + a*log|-------------|
2              \6*p*(a - 2*p)/
------------------------------
                     2        
        a*k*(a + 2*p)
alog⁡(a(a+2p)6p(a−2p))+a2−2pak(a+2p)2\frac{a \log{\left(\frac{a \left(a + 2 p\right)}{6 p \left(a - 2 p\right)} \right)} + \frac{a}{2} - 2 p}{a k \left(a + 2 p\right)^{2}} 
(a/2 - 2*p + a*log(a*(a + 2*p)/(6*p*(a - 2*p))))/(a*k*(a + 2*p)^2)
Respuesta numérica [src] 
0.25*log(((p + (a - 4*p)/6)*a)/(((a - 2*p)*p)))/(k*(p + 0.5*a)^2) + 0.333333333333333*(a - 4.0*p)/(a*k*(a + 2.0*p)*(0.666666666666667*a + 1.33333333333333*p))
0.25*log(((p + (a - 4*p)/6)*a)/(((a - 2*p)*p)))/(k*(p + 0.5*a)^2) + 0.333333333333333*(a - 4.0*p)/(a*k*(a + 2.0*p)*(0.666666666666667*a + 1.33333333333333*p))
Denominador racional [src] 
                                                   /        2                          \                /        2                          \                /        2                          \
                  2                  2        3    |       a                 a*p       |           2    |       a                 a*p       |           2    |       a                 a*p       |
- 12*k*p*(a + 2*p)  + 3*a*k*(a + 2*p)  + 6*k*a *log|---------------- + ----------------| + 24*a*k*p *log|---------------- + ----------------| + 24*k*p*a *log|---------------- + ----------------|
                                                   |  /     2      \     /     2      \|                |  /     2      \     /     2      \|                |  /     2      \     /     2      \|
                                                   \6*\- 2*p  + a*p/   3*\- 2*p  + a*p//                \6*\- 2*p  + a*p/   3*\- 2*p  + a*p//                \6*\- 2*p  + a*p/   3*\- 2*p  + a*p//
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                       2          3                                                                                               
                                                                                  3*a*k *(a + 2*p) *(2*a + 4*p)
6a3klog⁡(a26(ap−2p2)+ap3(ap−2p2))+24a2kplog⁡(a26(ap−2p2)+ap3(ap−2p2))+24akp2log⁡(a26(ap−2p2)+ap3(ap−2p2))+3ak(a+2p)2−12kp(a+2p)23ak2(a+2p)3(2a+4p)\frac{6 a^{3} k \log{\left(\frac{a^{2}}{6 \left(a p - 2 p^{2}\right)} + \frac{a p}{3 \left(a p - 2 p^{2}\right)} \right)} + 24 a^{2} k p \log{\left(\frac{a^{2}}{6 \left(a p - 2 p^{2}\right)} + \frac{a p}{3 \left(a p - 2 p^{2}\right)} \right)} + 24 a k p^{2} \log{\left(\frac{a^{2}}{6 \left(a p - 2 p^{2}\right)} + \frac{a p}{3 \left(a p - 2 p^{2}\right)} \right)} + 3 a k \left(a + 2 p\right)^{2} - 12 k p \left(a + 2 p\right)^{2}}{3 a k^{2} \left(a + 2 p\right)^{3} \left(2 a + 4 p\right)} 
(-12*k*p*(a + 2*p)^2 + 3*a*k*(a + 2*p)^2 + 6*k*a^3*log(a^2/(6*(-2*p^2 + a*p)) + a*p/(3*(-2*p^2 + a*p))) + 24*a*k*p^2*log(a^2/(6*(-2*p^2 + a*p)) + a*p/(3*(-2*p^2 + a*p))) + 24*k*p*a^2*log(a^2/(6*(-2*p^2 + a*p)) + a*p/(3*(-2*p^2 + a*p))))/(3*a*k^2*(a + 2*p)^3*(2*a + 4*p))
Combinatoria [src] 
 /                  /        2                          \\ 
 |                  |       a                 a*p       || 
-|-a + 4*p - 2*a*log|---------------- + ----------------|| 
 |                  |  /     2      \     /     2      \|| 
 \                  \6*\- 2*p  + a*p/   3*\- 2*p  + a*p/// 
-----------------------------------------------------------
                                     2                     
                      2*a*k*(a + 2*p)
−−2alog⁡(a26(ap−2p2)+ap3(ap−2p2))−a+4p2ak(a+2p)2- \frac{- 2 a \log{\left(\frac{a^{2}}{6 \left(a p - 2 p^{2}\right)} + \frac{a p}{3 \left(a p - 2 p^{2}\right)} \right)} - a + 4 p}{2 a k \left(a + 2 p\right)^{2}} 
-(-a + 4*p - 2*a*log(a^2/(6*(-2*p^2 + a*p)) + a*p/(3*(-2*p^2 + a*p))))/(2*a*k*(a + 2*p)^2)
Denominador común [src] 
 /                  /      2               \             \ 
 |                  |     a           2*a  |             | 
-|-a + 4*p - 2*a*log|------------ + -------| + 2*a*log(6)| 
 |                  |     2         a - 2*p|             | 
 \                  \- 2*p  + a*p          /             / 
-----------------------------------------------------------
                     3          2          2               
                2*k*a  + 8*a*k*p  + 8*k*p*a
−−2alog⁡(a2ap−2p2+2aa−2p)−a+2alog⁡(6)+4p2a3k+8a2kp+8akp2- \frac{- 2 a \log{\left(\frac{a^{2}}{a p - 2 p^{2}} + \frac{2 a}{a - 2 p} \right)} - a + 2 a \log{\left(6 \right)} + 4 p}{2 a^{3} k + 8 a^{2} k p + 8 a k p^{2}} 
-(-a + 4*p - 2*a*log(a^2/(-2*p^2 + a*p) + 2*a/(a - 2*p)) + 2*a*log(6))/(2*k*a^3 + 8*a*k*p^2 + 8*k*p*a^2)
Parte trigonométrica [src] 
   /   /p   a\ \                              
   | a*|- + -| |                              
   |   \3   6/ |                              
log|-----------|                              
   \p*(a - 2*p)/             a - 4*p          
---------------- + ---------------------------
             2                     /2*a   4*p\
  k*(a + 2*p)      3*a*k*(a + 2*p)*|--- + ---|
                                   \ 3     3 /
log⁡(a(a6+p3)p(a−2p))k(a+2p)2+a−4p3ak(2a3+4p3)(a+2p)\frac{\log{\left(\frac{a \left(\frac{a}{6} + \frac{p}{3}\right)}{p \left(a - 2 p\right)} \right)}}{k \left(a + 2 p\right)^{2}} + \frac{a - 4 p}{3 a k \left(\frac{2 a}{3} + \frac{4 p}{3}\right) \left(a + 2 p\right)} 
log(a*(p/3 + a/6)/(p*(a - 2*p)))/(k*(a + 2*p)^2) + (a - 4*p)/(3*a*k*(a + 2*p)*(2*a/3 + 4*p/3))
Potencias [src] 
   /   /p   a\ \                            
   | a*|- + -| |                            
   |   \3   6/ |             4*p   a        
log|-----------|           - --- + -        
   \p*(a - 2*p)/              3    3        
---------------- + -------------------------
             2                   /2*a   4*p\
  k*(a + 2*p)      a*k*(a + 2*p)*|--- + ---|
                                 \ 3     3 /
log⁡(a(a6+p3)p(a−2p))k(a+2p)2+a3−4p3ak(2a3+4p3)(a+2p)\frac{\log{\left(\frac{a \left(\frac{a}{6} + \frac{p}{3}\right)}{p \left(a - 2 p\right)} \right)}}{k \left(a + 2 p\right)^{2}} + \frac{\frac{a}{3} - \frac{4 p}{3}}{a k \left(\frac{2 a}{3} + \frac{4 p}{3}\right) \left(a + 2 p\right)} 
   /   /p   a\ \                              
   | a*|- + -| |                              
   |   \3   6/ |                              
log|-----------|                              
   \p*(a - 2*p)/             a - 4*p          
---------------- + ---------------------------
             2                     /2*a   4*p\
  k*(a + 2*p)      3*a*k*(a + 2*p)*|--- + ---|
                                   \ 3     3 /
log⁡(a(a6+p3)p(a−2p))k(a+2p)2+a−4p3ak(2a3+4p3)(a+2p)\frac{\log{\left(\frac{a \left(\frac{a}{6} + \frac{p}{3}\right)}{p \left(a - 2 p\right)} \right)}}{k \left(a + 2 p\right)^{2}} + \frac{a - 4 p}{3 a k \left(\frac{2 a}{3} + \frac{4 p}{3}\right) \left(a + 2 p\right)} 
log(a*(p/3 + a/6)/(p*(a - 2*p)))/(k*(a + 2*p)^2) + (a - 4*p)/(3*a*k*(a + 2*p)*(2*a/3 + 4*p/3))
Abrimos la expresión [src] 
   /  /    a - 4*p\\                                
   |a*|p + -------||                                
   |  \       6   /|                                
log|---------------|                                
   \  p*(a - 2*p)  /              a - 4*p           
-------------------- + -----------------------------
               2                       /    a - 4*p\
    k*(a + 2*p)        3*a*k*(a + 2*p)*|a - -------|
                                       \       3   /
log⁡(a(p+a−4p6)p(a−2p))k(a+2p)2+a−4p3ak(a+2p)(a−a−4p3)\frac{\log{\left(\frac{a \left(p + \frac{a - 4 p}{6}\right)}{p \left(a - 2 p\right)} \right)}}{k \left(a + 2 p\right)^{2}} + \frac{a - 4 p}{3 a k \left(a + 2 p\right) \left(a - \frac{a - 4 p}{3}\right)} 
log(a*(p + (a - 4*p)/6)/(p*(a - 2*p)))/(k*(a + 2*p)^2) + (a - 4*p)/(3*a*k*(a + 2*p)*(a - (a - 4*p)/3))
Compilar la expresión [src] 
   //    a - 4*p\  \                              
   ||p + -------|*a|                              
   |\       6   /  |                              
log|---------------|                              
   \  (a - 2*p)*p  /             a - 4*p          
-------------------- + ---------------------------
               2                       /2*a   4*p\
    k*(a + 2*p)        3*a*k*(a + 2*p)*|--- + ---|
                                       \ 3     3 /
log⁡(a(p+a−4p6)p(a−2p))k(a+2p)2+a−4p3ak(2a3+4p3)(a+2p)\frac{\log{\left(\frac{a \left(p + \frac{a - 4 p}{6}\right)}{p \left(a - 2 p\right)} \right)}}{k \left(a + 2 p\right)^{2}} + \frac{a - 4 p}{3 a k \left(\frac{2 a}{3} + \frac{4 p}{3}\right) \left(a + 2 p\right)} 
   //    a - 4*p\  \                            
   ||p + -------|*a|                            
   |\       6   /  |                            
log|---------------|                            
   \  (a - 2*p)*p  /            a - 4*p         
-------------------- + -------------------------
              2                      /2*a   4*p\
     (a + 2*p)         3*a*(a + 2*p)*|--- + ---|
                                     \ 3     3 /
------------------------------------------------
                       k
log⁡(a(p+a−4p6)p(a−2p))(a+2p)2+a−4p3a(2a3+4p3)(a+2p)k\frac{\frac{\log{\left(\frac{a \left(p + \frac{a - 4 p}{6}\right)}{p \left(a - 2 p\right)} \right)}}{\left(a + 2 p\right)^{2}} + \frac{a - 4 p}{3 a \left(\frac{2 a}{3} + \frac{4 p}{3}\right) \left(a + 2 p\right)}}{k} 
(log(((p + (a - 4*p)/6)*a)/(((a - 2*p)*p)))/(a + 2*p)^2 + (a - 4*p)/(3*a*(a + 2*p)*(2*a/3 + 4*p/3)))/k
Unión de expresiones racionales [src] 
                 / a*(a + 2*p) \
a - 4*p + 2*a*log|-------------|
                 \6*p*(a - 2*p)/
--------------------------------
                       2        
        2*a*k*(a + 2*p)
2alog⁡(a(a+2p)6p(a−2p))+a−4p2ak(a+2p)2\frac{2 a \log{\left(\frac{a \left(a + 2 p\right)}{6 p \left(a - 2 p\right)} \right)} + a - 4 p}{2 a k \left(a + 2 p\right)^{2}} 
(a - 4*p + 2*a*log(a*(a + 2*p)/(6*p*(a - 2*p))))/(2*a*k*(a + 2*p)^2)
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