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Simplificación de expresiones/ Descomposición en fracciones simples/ abs(((2*a^(1/4))*(2*d^(1/4)))^2)/((a+b)/(sqrt(a)/sqrt(b)))

¿Cómo vas a descomponer esta abs(((2*a^(1/4))*(2*d^(1/4)))^2)/((a+b)/(sqrt(a)/sqrt(b))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
|                 2|
|/  4 ___   4 ___\ |
|\2*\/ a *2*\/ d / |
--------------------
     / a + b \      
     |-------|      
     |/  ___\|      
     ||\/ a ||      
     ||-----||      
     ||  ___||      
     \\\/ b //
$$\frac{\left|{\left(2 \sqrt[4]{a} 2 \sqrt[4]{d}\right)^{2}}\right|}{\frac{1}{\sqrt{a} \frac{1}{\sqrt{b}}} \left(a + b\right)}$$ 
Abs(((2*a^(1/4))*(2*d^(1/4)))^2)/(((a + b)/((sqrt(a)/sqrt(b)))))
Simplificación general [src] 
     ___ |  ___   ___|
16*\/ a *|\/ a *\/ d |
----------------------
      ___             
    \/ b *(a + b)
$$\frac{16 \sqrt{a} \left|{\sqrt{a} \sqrt{d}}\right|}{\sqrt{b} \left(a + b\right)}$$ 
16*sqrt(a)*Abs(sqrt(a)*sqrt(d))/(sqrt(b)*(a + b))
Respuesta numérica [src] 
a^0.5*b^(-0.5)*Abs(((2*a^(1/4))*(2*d^(1/4)))^2)/(a + b)
a^0.5*b^(-0.5)*Abs(((2*a^(1/4))*(2*d^(1/4)))^2)/(a + b)
Unión de expresiones racionales [src] 
     ___ |  ___   ___|
16*\/ a *|\/ a *\/ d |
----------------------
      ___             
    \/ b *(a + b)
$$\frac{16 \sqrt{a} \left|{\sqrt{a} \sqrt{d}}\right|}{\sqrt{b} \left(a + b\right)}$$ 
16*sqrt(a)*Abs(sqrt(a)*sqrt(d))/(sqrt(b)*(a + b))
Compilar la expresión [src] 
      |                 2|
  ___ |/  4 ___   4 ___\ |
\/ a *|\2*\/ a *2*\/ d / |
--------------------------
        ___               
      \/ b *(a + b)
$$\frac{\sqrt{a} \left|{\left(2 \sqrt[4]{a} 2 \sqrt[4]{d}\right)^{2}}\right|}{\sqrt{b} \left(a + b\right)}$$ 
sqrt(a)*Abs(((2*a^(1/4))*(2*d^(1/4)))^2)/(sqrt(b)*(a + b))
Abrimos la expresión [src] 
     ___ |  ___| |  ___|
16*\/ a *|\/ a |*|\/ d |
------------------------
       ___              
     \/ b *(a + b)
$$\frac{16 \sqrt{a} \left|{\sqrt{a}}\right| \left|{\sqrt{d}}\right|}{\sqrt{b} \left(a + b\right)}$$ 
16*sqrt(a)*Abs(sqrt(a))*Abs(sqrt(d))/(sqrt(b)*(a + b))
Parte trigonométrica [src] 
     ___ |  ___   ___|
16*\/ a *|\/ a *\/ d |
----------------------
      ___             
    \/ b *(a + b)
$$\frac{16 \sqrt{a} \left|{\sqrt{a} \sqrt{d}}\right|}{\sqrt{b} \left(a + b\right)}$$ 
16*sqrt(a)*Abs(sqrt(a)*sqrt(d))/(sqrt(b)*(a + b))
Denominador racional [src] 
     ___ |  ___   ___|
16*\/ a *|\/ a *\/ d |
----------------------
      ___             
    \/ b *(a + b)
$$\frac{16 \sqrt{a} \left|{\sqrt{a} \sqrt{d}}\right|}{\sqrt{b} \left(a + b\right)}$$ 
16*sqrt(a)*Abs(sqrt(a)*sqrt(d))/(sqrt(b)*(a + b))
Combinatoria [src] 
     ___ |  ___   ___|
16*\/ a *|\/ a *\/ d |
----------------------
      ___             
    \/ b *(a + b)
$$\frac{16 \sqrt{a} \left|{\sqrt{a} \sqrt{d}}\right|}{\sqrt{b} \left(a + b\right)}$$ 
16*sqrt(a)*Abs(sqrt(a)*sqrt(d))/(sqrt(b)*(a + b))
Potencias [src] 
     ___ |  ___   ___|
16*\/ a *|\/ a *\/ d |
----------------------
      ___             
    \/ b *(a + b)
$$\frac{16 \sqrt{a} \left|{\sqrt{a} \sqrt{d}}\right|}{\sqrt{b} \left(a + b\right)}$$ 
     ___ |  _____|
16*\/ a *|\/ a*d |
------------------
    ___           
  \/ b *(a + b)
$$\frac{16 \sqrt{a} \left|{\sqrt{a d}}\right|}{\sqrt{b} \left(a + b\right)}$$ 
16*sqrt(a)*Abs(sqrt(a*d))/(sqrt(b)*(a + b))
Denominador común [src] 
     ___ |  ___   ___|
16*\/ a *|\/ a *\/ d |
----------------------
     3/2       ___    
    b    + a*\/ b
$$\frac{16 \sqrt{a} \left|{\sqrt{a} \sqrt{d}}\right|}{a \sqrt{b} + b^{\frac{3}{2}}}$$ 
16*sqrt(a)*Abs(sqrt(a)*sqrt(d))/(b^(3/2) + a*sqrt(b))
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