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Simplificación de expresiones/ Descomposición en fracciones simples/ (c*(v/k+1)+t)/((n+k)*(v/k+1)-k)

¿Cómo vas a descomponer esta (c*(v/k+1)+t)/((n+k)*(v/k+1)-k) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     /v    \       
   c*|- + 1| + t   
     \k    /       
-------------------
        /v    \    
(n + k)*|- + 1| - k
        \k    /
c(1+vk)+t−k+(1+vk)(k+n)\frac{c \left(1 + \frac{v}{k}\right) + t}{- k + \left(1 + \frac{v}{k}\right) \left(k + n\right)} 
(c*(v/k + 1) + t)/((n + k)*(v/k + 1) - k)
Simplificación general [src] 
-(c*(k + v) + k*t)  
--------------------
 2                  
k  - (k + n)*(k + v)
−c(k+v)+ktk2−(k+n)(k+v)- \frac{c \left(k + v\right) + k t}{k^{2} - \left(k + n\right) \left(k + v\right)} 
-(c*(k + v) + k*t)/(k^2 - (k + n)*(k + v))
Combinatoria [src] 
c*k + c*v + k*t
---------------
k*n + k*v + n*v
ck+cv+ktkn+kv+nv\frac{c k + c v + k t}{k n + k v + n v} 
(c*k + c*v + k*t)/(k*n + k*v + n*v)
Denominador común [src] 
c*k + c*v + k*t
---------------
k*n + k*v + n*v
ck+cv+ktkn+kv+nv\frac{c k + c v + k t}{k n + k v + n v} 
(c*k + c*v + k*t)/(k*n + k*v + n*v)
Denominador racional [src] 
c*k + c*v + k*t
---------------
k*n + k*v + n*v
ck+cv+ktkn+kv+nv\frac{c k + c v + k t}{k n + k v + n v} 
(c*k + c*v + k*t)/(k*n + k*v + n*v)
Unión de expresiones racionales [src] 
   c*(k + v) + k*t    
----------------------
   2                  
- k  + (k + n)*(k + v)
c(k+v)+kt−k2+(k+n)(k+v)\frac{c \left(k + v\right) + k t}{- k^{2} + \left(k + n\right) \left(k + v\right)} 
(c*(k + v) + k*t)/(-k^2 + (k + n)*(k + v))
Respuesta numérica [src] 
(t + c*(1.0 + v/k))/(-k + (1.0 + v/k)*(k + n))
(t + c*(1.0 + v/k))/(-k + (1.0 + v/k)*(k + n))
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