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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(40*pi*t+pi)/(80*pi)+sin(32*pi*t+pi)/(64*pi)

¿Cómo vas a descomponer esta sin(40*pi*t+pi)/(80*pi)+sin(32*pi*t+pi)/(64*pi) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
sin(40*pi*t + pi)   sin(32*pi*t + pi)
----------------- + -----------------
      80*pi               64*pi
sin⁡(32πt+π)64π+sin⁡(40πt+π)80π\frac{\sin{\left(32 \pi t + \pi \right)}}{64 \pi} + \frac{\sin{\left(40 \pi t + \pi \right)}}{80 \pi} 
sin((40*pi)*t + pi)/((80*pi)) + sin((32*pi)*t + pi)/((64*pi))
Simplificación general [src] 
 /sin(32*pi*t)   sin(40*pi*t)\ 
-|------------ + ------------| 
 \     64             80     / 
-------------------------------
               pi
−sin⁡(32πt)64+sin⁡(40πt)80π- \frac{\frac{\sin{\left(32 \pi t \right)}}{64} + \frac{\sin{\left(40 \pi t \right)}}{80}}{\pi} 
-(sin(32*pi*t)/64 + sin(40*pi*t)/80)/pi
Respuesta numérica [src] 
0.00397887357729738*sin((40*pi)*t + pi) + 0.00497359197162173*sin((32*pi)*t + pi)
0.00397887357729738*sin((40*pi)*t + pi) + 0.00497359197162173*sin((32*pi)*t + pi)
Denominador racional [src] 
-80*pi*sin(32*pi*t) - 64*pi*sin(40*pi*t)
----------------------------------------
                       2                
                5120*pi
−80πsin⁡(32πt)−64πsin⁡(40πt)5120π2\frac{- 80 \pi \sin{\left(32 \pi t \right)} - 64 \pi \sin{\left(40 \pi t \right)}}{5120 \pi^{2}} 
(-80*pi*sin(32*pi*t) - 64*pi*sin(40*pi*t))/(5120*pi^2)
Unión de expresiones racionales [src] 
4*sin(pi*(1 + 40*t)) + 5*sin(pi*(1 + 32*t))
-------------------------------------------
                   320*pi
5sin⁡(π(32t+1))+4sin⁡(π(40t+1))320π\frac{5 \sin{\left(\pi \left(32 t + 1\right) \right)} + 4 \sin{\left(\pi \left(40 t + 1\right) \right)}}{320 \pi} 
(4*sin(pi*(1 + 40*t)) + 5*sin(pi*(1 + 32*t)))/(320*pi)
Denominador común [src] 
-(4*sin(40*pi*t) + 5*sin(32*pi*t)) 
-----------------------------------
               320*pi
−5sin⁡(32πt)+4sin⁡(40πt)320π- \frac{5 \sin{\left(32 \pi t \right)} + 4 \sin{\left(40 \pi t \right)}}{320 \pi} 
-(4*sin(40*pi*t) + 5*sin(32*pi*t))/(320*pi)
Potencias [src] 
  sin(32*pi*t)   sin(40*pi*t)
- ------------ - ------------
     64*pi          80*pi
−sin⁡(32πt)64π−sin⁡(40πt)80π- \frac{\sin{\left(32 \pi t \right)}}{64 \pi} - \frac{\sin{\left(40 \pi t \right)}}{80 \pi} 
    /   I*(-pi - 32*pi*t)    I*(pi + 32*pi*t)\     /   I*(-pi - 40*pi*t)    I*(pi + 40*pi*t)\
  I*\- e                  + e                /   I*\- e                  + e                /
- -------------------------------------------- - --------------------------------------------
                     128*pi                                         160*pi
−i(−ei(−40πt−π)+ei(40πt+π))160π−i(−ei(−32πt−π)+ei(32πt+π))128π- \frac{i \left(- e^{i \left(- 40 \pi t - \pi\right)} + e^{i \left(40 \pi t + \pi\right)}\right)}{160 \pi} - \frac{i \left(- e^{i \left(- 32 \pi t - \pi\right)} + e^{i \left(32 \pi t + \pi\right)}\right)}{128 \pi} 
-i*(-exp(i*(-pi - 32*pi*t)) + exp(i*(pi + 32*pi*t)))/(128*pi) - i*(-exp(i*(-pi - 40*pi*t)) + exp(i*(pi + 40*pi*t)))/(160*pi)
Abrimos la expresión [src] 
  sin(32*pi*t)   sin(40*pi*t)
- ------------ - ------------
     64*pi          80*pi
−sin⁡(32πt)64π−sin⁡(40πt)80π- \frac{\sin{\left(32 \pi t \right)}}{64 \pi} - \frac{\sin{\left(40 \pi t \right)}}{80 \pi} 
-sin((32*pi)*t)/(64*pi) - sin((40*pi)*t)/(80*pi)
Combinatoria [src] 
-(4*sin(40*pi*t) + 5*sin(32*pi*t)) 
-----------------------------------
               320*pi
−5sin⁡(32πt)+4sin⁡(40πt)320π- \frac{5 \sin{\left(32 \pi t \right)} + 4 \sin{\left(40 \pi t \right)}}{320 \pi} 
-(4*sin(40*pi*t) + 5*sin(32*pi*t))/(320*pi)
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