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