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¿Cómo vas a descomponer esta sqrt(x-4)*(-25+3*x^2)+(x^3-25*x)/(2*sqrt(x-4)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
                           3        
  _______ /         2\    x  - 25*x 
\/ x - 4 *\-25 + 3*x / + -----------
                             _______
                         2*\/ x - 4 
$$\sqrt{x - 4} \left(3 x^{2} - 25\right) + \frac{x^{3} - 25 x}{2 \sqrt{x - 4}}$$
sqrt(x - 4)*(-25 + 3*x^2) + (x^3 - 25*x)/((2*sqrt(x - 4)))
Simplificación general [src]
                 2      3
200 - 75*x - 24*x  + 7*x 
-------------------------
           ________      
       2*\/ -4 + x       
$$\frac{7 x^{3} - 24 x^{2} - 75 x + 200}{2 \sqrt{x - 4}}$$
(200 - 75*x - 24*x^2 + 7*x^3)/(2*sqrt(-4 + x))
Respuesta numérica [src]
0.25*(-1 + 0.25*x)^(-0.5)*(x^3 - 25.0*x) + 2.0*(-1 + 0.25*x)^0.5*(-25.0 + 3.0*x^2)
0.25*(-1 + 0.25*x)^(-0.5)*(x^3 - 25.0*x) + 2.0*(-1 + 0.25*x)^0.5*(-25.0 + 3.0*x^2)
Denominador común [src]
                 2      3
200 - 75*x - 24*x  + 7*x 
-------------------------
           ________      
       2*\/ -4 + x       
$$\frac{7 x^{3} - 24 x^{2} - 75 x + 200}{2 \sqrt{x - 4}}$$
(200 - 75*x - 24*x^2 + 7*x^3)/(2*sqrt(-4 + x))
Combinatoria [src]
                 2      3
200 - 75*x - 24*x  + 7*x 
-------------------------
           ________      
       2*\/ -4 + x       
$$\frac{7 x^{3} - 24 x^{2} - 75 x + 200}{2 \sqrt{x - 4}}$$
(200 - 75*x - 24*x^2 + 7*x^3)/(2*sqrt(-4 + x))
Denominador racional [src]
      ________          ________       2   ________      3   ________
200*\/ -4 + x  - 75*x*\/ -4 + x  - 24*x *\/ -4 + x  + 7*x *\/ -4 + x 
---------------------------------------------------------------------
                               -8 + 2*x                              
$$\frac{7 x^{3} \sqrt{x - 4} - 24 x^{2} \sqrt{x - 4} - 75 x \sqrt{x - 4} + 200 \sqrt{x - 4}}{2 x - 8}$$
(200*sqrt(-4 + x) - 75*x*sqrt(-4 + x) - 24*x^2*sqrt(-4 + x) + 7*x^3*sqrt(-4 + x))/(-8 + 2*x)
Unión de expresiones racionales [src]
  /       2\     /         2\         
x*\-25 + x / + 2*\-25 + 3*x /*(-4 + x)
--------------------------------------
                 ________             
             2*\/ -4 + x              
$$\frac{x \left(x^{2} - 25\right) + 2 \left(x - 4\right) \left(3 x^{2} - 25\right)}{2 \sqrt{x - 4}}$$
(x*(-25 + x^2) + 2*(-25 + 3*x^2)*(-4 + x))/(2*sqrt(-4 + x))
Potencias [src]
                           3        
                          x    25*x 
                          -- - ---- 
  ________ /         2\   2     2   
\/ -4 + x *\-25 + 3*x / + ----------
                            ________
                          \/ -4 + x 
$$\sqrt{x - 4} \left(3 x^{2} - 25\right) + \frac{\frac{x^{3}}{2} - \frac{25 x}{2}}{\sqrt{x - 4}}$$
sqrt(-4 + x)*(-25 + 3*x^2) + (x^3/2 - 25*x/2)/sqrt(-4 + x)