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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt((625*x^4+25*10^10*x^2)/(1+25*x^2)^2)

¿Cómo vas a descomponer esta sqrt((625*x^4+25*10^10*x^2)/(1+25*x^2)^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
       __________________________
      /      4                 2 
     /  625*x  + 250000000000*x  
    /   ------------------------ 
   /                     2       
  /           /        2\        
\/            \1 + 25*x /
$$\sqrt{\frac{625 x^{4} + 250000000000 x^{2}}{\left(25 x^{2} + 1\right)^{2}}}$$ 
sqrt((625*x^4 + 250000000000*x^2)/(1 + 25*x^2)^2)
Simplificación general [src] 
          _____________________
         /  2 /             2\ 
        /  x *\400000000 + x / 
25*    /   ------------------- 
      /                   2    
     /         /        2\     
   \/          \1 + 25*x /
$$25 \sqrt{\frac{x^{2} \left(x^{2} + 400000000\right)}{\left(25 x^{2} + 1\right)^{2}}}$$ 
25*sqrt(x^2*(400000000 + x^2)/(1 + 25*x^2)^2)
Descomposición de una fracción [src] 
sqrt(625*x^4/(1 + 50*x^2 + 625*x^4) + 250000000000*x^2/(1 + 50*x^2 + 625*x^4))
$$\sqrt{\frac{625 x^{4}}{625 x^{4} + 50 x^{2} + 1} + \frac{250000000000 x^{2}}{625 x^{4} + 50 x^{2} + 1}}$$ 
      _________________________________________
     /            4                        2   
    /        625*x           250000000000*x    
   /   ------------------ + ------------------ 
  /            2        4           2        4 
\/     1 + 50*x  + 625*x    1 + 50*x  + 625*x
Respuesta numérica [src] 
0.04*((625.0*x^4 + 250000000000.0*x^2)/(0.04 + x^2)^2)^0.5
0.04*((625.0*x^4 + 250000000000.0*x^2)/(0.04 + x^2)^2)^0.5
Abrimos la expresión [src] 
      ______________    __________________________
     /      1          /      4                 2 
    /  ------------ *\/  625*x  + 250000000000*x  
   /              2                               
  /    /        2\                                
\/     \1 + 25*x /
$$\sqrt{625 x^{4} + 250000000000 x^{2}} \sqrt{\frac{1}{\left(25 x^{2} + 1\right)^{2}}}$$ 
sqrt(1/((1 + 25*x^2)^2))*sqrt(625*x^4 + 250000000000*x^2)
Unión de expresiones racionales [src] 
          _____________________
         /  2 /             2\ 
        /  x *\400000000 + x / 
25*    /   ------------------- 
      /                   2    
     /         /        2\     
   \/          \1 + 25*x /
$$25 \sqrt{\frac{x^{2} \left(x^{2} + 400000000\right)}{\left(25 x^{2} + 1\right)^{2}}}$$ 
25*sqrt(x^2*(400000000 + x^2)/(1 + 25*x^2)^2)
Denominador común [src] 
         _________________________________________
        /          4                         2    
       /          x               400000000*x     
25*   /   ------------------ + ------------------ 
     /            2        4           2        4 
   \/     1 + 50*x  + 625*x    1 + 50*x  + 625*x
$$25 \sqrt{\frac{x^{4}}{625 x^{4} + 50 x^{2} + 1} + \frac{400000000 x^{2}}{625 x^{4} + 50 x^{2} + 1}}$$ 
25*sqrt(x^4/(1 + 50*x^2 + 625*x^4) + 400000000*x^2/(1 + 50*x^2 + 625*x^4))
Combinatoria [src] 
         _____________________
        /  2 /             2\ 
       /  x *\400000000 + x / 
25*   /   ------------------- 
     /             2        4 
   \/      1 + 50*x  + 625*x
$$25 \sqrt{\frac{x^{2} \left(x^{2} + 400000000\right)}{625 x^{4} + 50 x^{2} + 1}}$$ 
25*sqrt(x^2*(400000000 + x^2)/(1 + 50*x^2 + 625*x^4))
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