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¿Cómo vas a descomponer esta pi*sin(pi/(z+1))/(z+1)^2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
      /  pi \
pi*sin|-----|
      \z + 1/
-------------
          2  
   (z + 1)   
$$\frac{\pi \sin{\left(\frac{\pi}{z + 1} \right)}}{\left(z + 1\right)^{2}}$$
(pi*sin(pi/(z + 1)))/(z + 1)^2
Respuesta numérica [src]
3.14159265358979*sin(pi/(z + 1))/(1.0 + z)^2
3.14159265358979*sin(pi/(z + 1))/(1.0 + z)^2
Denominador común [src]
      /  pi \
pi*sin|-----|
      \1 + z/
-------------
      2      
 1 + z  + 2*z
$$\frac{\pi \sin{\left(\frac{\pi}{z + 1} \right)}}{z^{2} + 2 z + 1}$$
pi*sin(pi/(1 + z))/(1 + z^2 + 2*z)
Potencias [src]
      /   -pi*I      pi*I\ 
      |   ------    -----| 
      |   1 + z     1 + z| 
-pi*I*\- e       + e     / 
---------------------------
                  2        
         2*(1 + z)         
$$- \frac{i \pi \left(e^{\frac{i \pi}{z + 1}} - e^{- \frac{i \pi}{z + 1}}\right)}{2 \left(z + 1\right)^{2}}$$
-pi*i*(-exp(-pi*i/(1 + z)) + exp(pi*i/(1 + z)))/(2*(1 + z)^2)
Abrimos la expresión [src]
      /  pi \
pi*sin|-----|
      \z + 1/
-------------
      2      
 1 + z  + 2*z
$$\frac{\pi \sin{\left(\frac{\pi}{z + 1} \right)}}{z^{2} + 2 z + 1}$$
pi*sin(pi/(z + 1))/(1 + z^2 + 2*z)
Parte trigonométrica [src]
      /  pi     pi \
pi*cos|- -- + -----|
      \  2    1 + z/
--------------------
             2      
      (1 + z)       
$$\frac{\pi \cos{\left(- \frac{\pi}{2} + \frac{\pi}{z + 1} \right)}}{\left(z + 1\right)^{2}}$$
         pi        
-------------------
       2    /  pi \
(1 + z) *csc|-----|
            \1 + z/
$$\frac{\pi}{\left(z + 1\right)^{2} \csc{\left(\frac{\pi}{z + 1} \right)}}$$
            pi            
--------------------------
       2    /  pi     pi \
(1 + z) *sec|- -- + -----|
            \  2    1 + z/
$$\frac{\pi}{\left(z + 1\right)^{2} \sec{\left(- \frac{\pi}{2} + \frac{\pi}{z + 1} \right)}}$$
             /    pi   \      
     2*pi*cot|---------|      
             \2*(1 + z)/      
------------------------------
       2 /       2/    pi   \\
(1 + z) *|1 + cot |---------||
         \        \2*(1 + z)//
$$\frac{2 \pi \cot{\left(\frac{\pi}{2 \left(z + 1\right)} \right)}}{\left(z + 1\right)^{2} \left(\cot^{2}{\left(\frac{\pi}{2 \left(z + 1\right)} \right)} + 1\right)}$$
             /    pi   \      
     2*pi*tan|---------|      
             \2*(1 + z)/      
------------------------------
       2 /       2/    pi   \\
(1 + z) *|1 + tan |---------||
         \        \2*(1 + z)//
$$\frac{2 \pi \tan{\left(\frac{\pi}{2 \left(z + 1\right)} \right)}}{\left(z + 1\right)^{2} \left(\tan^{2}{\left(\frac{\pi}{2 \left(z + 1\right)} \right)} + 1\right)}$$
2*pi*tan(pi/(2*(1 + z)))/((1 + z)^2*(1 + tan(pi/(2*(1 + z)))^2))