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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
      __________________________
     /      4                 2 
    /  625*x  + 250000000000*x  
   /   ------------------------ 
  /                   2         
\/            1 + 25*x
$$\sqrt{\frac{625 x^{4} + 250000000000 x^{2}}{25 x^{2} + 1}}$$ 
sqrt((625*x^4 + 250000000000*x^2)/(1 + 25*x^2))
Descomposición de una fracción [src] 
sqrt(625*x^4/(1 + 25*x^2) + 250000000000*x^2/(1 + 25*x^2))
$$\sqrt{\frac{625 x^{4}}{25 x^{2} + 1} + \frac{250000000000 x^{2}}{25 x^{2} + 1}}$$ 
      _____________________________
     /        4                  2 
    /    625*x     250000000000*x  
   /   --------- + --------------- 
  /            2              2    
\/     1 + 25*x       1 + 25*x
Simplificación general [src] 
         _____________________
        /  2 /             2\ 
       /  x *\400000000 + x / 
25*   /   ------------------- 
     /                 2      
   \/          1 + 25*x
$$25 \sqrt{\frac{x^{2} \left(x^{2} + 400000000\right)}{25 x^{2} + 1}}$$ 
25*sqrt(x^2*(400000000 + x^2)/(1 + 25*x^2))
Abrimos la expresión [src] 
     ___________    __________________________
    /     1        /      4                 2 
   /  --------- *\/  625*x  + 250000000000*x  
  /           2                               
\/    1 + 25*x
$$\sqrt{625 x^{4} + 250000000000 x^{2}} \sqrt{\frac{1}{25 x^{2} + 1}}$$ 
sqrt(1/(1 + 25*x^2))*sqrt(625*x^4 + 250000000000*x^2)
Denominador común [src] 
         __________________________
        /      4                 2 
       /      x       400000000*x  
25*   /   --------- + ------------ 
     /            2            2   
   \/     1 + 25*x     1 + 25*x
$$25 \sqrt{\frac{x^{4}}{25 x^{2} + 1} + \frac{400000000 x^{2}}{25 x^{2} + 1}}$$ 
25*sqrt(x^4/(1 + 25*x^2) + 400000000*x^2/(1 + 25*x^2))
Respuesta numérica [src] 
((625.0*x^4 + 250000000000.0*x^2)/(1.0 + 25.0*x^2))^0.5
((625.0*x^4 + 250000000000.0*x^2)/(1.0 + 25.0*x^2))^0.5
Combinatoria [src] 
         _____________________
        /  2 /             2\ 
       /  x *\400000000 + x / 
25*   /   ------------------- 
     /                 2      
   \/          1 + 25*x
$$25 \sqrt{\frac{x^{2} \left(x^{2} + 400000000\right)}{25 x^{2} + 1}}$$ 
25*sqrt(x^2*(400000000 + x^2)/(1 + 25*x^2))
Unión de expresiones racionales [src] 
         _____________________
        /  2 /             2\ 
       /  x *\400000000 + x / 
25*   /   ------------------- 
     /                 2      
   \/          1 + 25*x
$$25 \sqrt{\frac{x^{2} \left(x^{2} + 400000000\right)}{25 x^{2} + 1}}$$ 
25*sqrt(x^2*(400000000 + x^2)/(1 + 25*x^2))
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