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Simplificación de expresiones/ Descomposición en fracciones simples/ 2*(3*x^2/(x-1)^2-4*x/(x-1)+1)/(x-1)^2

¿Cómo vas a descomponer esta 2*(3*x^2/(x-1)^2-4*x/(x-1)+1)/(x-1)^2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  /     2              \
  |  3*x       4*x     |
2*|-------- - ----- + 1|
  |       2   x - 1    |
  \(x - 1)             /
------------------------
               2        
        (x - 1)
$$\frac{2 \left(\left(- \frac{4 x}{x - 1} + \frac{3 x^{2}}{\left(x - 1\right)^{2}}\right) + 1\right)}{\left(x - 1\right)^{2}}$$ 
(2*((3*x^2)/(x - 1)^2 - 4*x/(x - 1) + 1))/(x - 1)^2
Simplificación general [src] 
  /        2      2               \
2*\(-1 + x)  + 3*x  - 4*x*(-1 + x)/
-----------------------------------
                     4             
             (-1 + x)
$$\frac{2 \left(3 x^{2} - 4 x \left(x - 1\right) + \left(x - 1\right)^{2}\right)}{\left(x - 1\right)^{4}}$$ 
2*((-1 + x)^2 + 3*x^2 - 4*x*(-1 + x))/(-1 + x)^4
Descomposición de una fracción [src] 
4/(-1 + x)^3 + 6/(-1 + x)^4
$$\frac{4}{\left(x - 1\right)^{3}} + \frac{6}{\left(x - 1\right)^{4}}$$ 
    4           6    
--------- + ---------
        3           4
(-1 + x)    (-1 + x)
Respuesta numérica [src] 
(2.0 + 6.0*x^2/(-1.0 + x)^2 - 8.0*x/(-1.0 + x))/(-1.0 + x)^2
(2.0 + 6.0*x^2/(-1.0 + x)^2 - 8.0*x/(-1.0 + x))/(-1.0 + x)^2
Denominador racional [src] 
          3               2      2         
2*(-1 + x)  - 8*x*(-1 + x)  + 6*x *(-1 + x)
-------------------------------------------
                         5                 
                 (-1 + x)
$$\frac{6 x^{2} \left(x - 1\right) - 8 x \left(x - 1\right)^{2} + 2 \left(x - 1\right)^{3}}{\left(x - 1\right)^{5}}$$ 
(2*(-1 + x)^3 - 8*x*(-1 + x)^2 + 6*x^2*(-1 + x))/(-1 + x)^5
Denominador común [src] 
         2 + 4*x          
--------------------------
     4            3      2
1 + x  - 4*x - 4*x  + 6*x
$$\frac{4 x + 2}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1}$$ 
(2 + 4*x)/(1 + x^4 - 4*x - 4*x^3 + 6*x^2)
Compilar la expresión [src] 
                   2  
     8*x        6*x   
2 - ------ + ---------
    -1 + x           2
             (-1 + x) 
----------------------
              2       
      (-1 + x)
$$\frac{\frac{6 x^{2}}{\left(x - 1\right)^{2}} - \frac{8 x}{x - 1} + 2}{\left(x - 1\right)^{2}}$$ 
(2 - 8*x/(-1 + x) + 6*x^2/(-1 + x)^2)/(-1 + x)^2
Unión de expresiones racionales [src] 
  /        2            \
2*\(-1 + x)  + x*(4 - x)/
-------------------------
                4        
        (-1 + x)
$$\frac{2 \left(x \left(4 - x\right) + \left(x - 1\right)^{2}\right)}{\left(x - 1\right)^{4}}$$ 
2*((-1 + x)^2 + x*(4 - x))/(-1 + x)^4
Combinatoria [src] 
2*(1 + 2*x)
-----------
         4 
 (-1 + x)
$$\frac{2 \left(2 x + 1\right)}{\left(x - 1\right)^{4}}$$ 
2*(1 + 2*x)/(-1 + x)^4
Potencias [src] 
                   2  
     8*x        6*x   
2 - ------ + ---------
    -1 + x           2
             (-1 + x) 
----------------------
              2       
      (-1 + x)
$$\frac{\frac{6 x^{2}}{\left(x - 1\right)^{2}} - \frac{8 x}{x - 1} + 2}{\left(x - 1\right)^{2}}$$ 
(2 - 8*x/(-1 + x) + 6*x^2/(-1 + x)^2)/(-1 + x)^2
Parte trigonométrica [src] 
                   2  
     8*x        6*x   
2 - ------ + ---------
    -1 + x           2
             (-1 + x) 
----------------------
              2       
      (-1 + x)
$$\frac{\frac{6 x^{2}}{\left(x - 1\right)^{2}} - \frac{8 x}{x - 1} + 2}{\left(x - 1\right)^{2}}$$ 
(2 - 8*x/(-1 + x) + 6*x^2/(-1 + x)^2)/(-1 + x)^2
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