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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(14-6*sqrt(5))-1/(2-sqrt(5))*sqrt(14-6*sqrt(5))-1/(2-sqrt(5))

¿Cómo vas a descomponer esta sqrt(14-6*sqrt(5))-1/(2-sqrt(5))*sqrt(14-6*sqrt(5))-1/(2-sqrt(5)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                       ______________            
   ______________     /          ___             
  /          ___    \/  14 - 6*\/ 5         1    
\/  14 - 6*\/ 5   - ----------------- - ---------
                              ___             ___
                        2 - \/ 5        2 - \/ 5
(14−65−14−652−5)−12−5\left(\sqrt{14 - 6 \sqrt{5}} - \frac{\sqrt{14 - 6 \sqrt{5}}}{2 - \sqrt{5}}\right) - \frac{1}{2 - \sqrt{5}} 
sqrt(14 - 6*sqrt(5)) - sqrt(14 - 6*sqrt(5))/(2 - sqrt(5)) - 1/(2 - sqrt(5))
Simplificación general [src] 
                                   ______________
   ______________                 /          ___ 
  /          ___        1       \/  14 - 6*\/ 5  
\/  14 - 6*\/ 5   - --------- - -----------------
                          ___             ___    
                    2 - \/ 5        2 - \/ 5
14−65−14−652−5−12−5\sqrt{14 - 6 \sqrt{5}} - \frac{\sqrt{14 - 6 \sqrt{5}}}{2 - \sqrt{5}} - \frac{1}{2 - \sqrt{5}} 
sqrt(14 - 6*sqrt(5)) - 1/(2 - sqrt(5)) - sqrt(14 - 6*sqrt(5))/(2 - sqrt(5))
Respuesta numérica [src] 
8.23606797749979
8.23606797749979
Parte trigonométrica [src] 
                                   ______________
   ______________                 /          ___ 
  /          ___        1       \/  14 - 6*\/ 5  
\/  14 - 6*\/ 5   - --------- - -----------------
                          ___             ___    
                    2 - \/ 5        2 - \/ 5
14−65−14−652−5−12−5\sqrt{14 - 6 \sqrt{5}} - \frac{\sqrt{14 - 6 \sqrt{5}}}{2 - \sqrt{5}} - \frac{1}{2 - \sqrt{5}} 
sqrt(14 - 6*sqrt(5)) - 1/(2 - sqrt(5)) - sqrt(14 - 6*sqrt(5))/(2 - sqrt(5))
Denominador racional [src] 
                 ______________            ______________
      ___       /          ___      ___   /          ___ 
2 + \/ 5  + 3*\/  14 - 6*\/ 5   + \/ 5 *\/  14 - 6*\/ 5
514−65+2+5+314−65\sqrt{5} \sqrt{14 - 6 \sqrt{5}} + 2 + \sqrt{5} + 3 \sqrt{14 - 6 \sqrt{5}} 
2 + sqrt(5) + 3*sqrt(14 - 6*sqrt(5)) + sqrt(5)*sqrt(14 - 6*sqrt(5))
Combinatoria [src] 
              _____________            _____________
      ____   /         ___      ___   /         ___ 
1 + \/ 10 *\/  7 - 3*\/ 5   - \/ 2 *\/  7 - 3*\/ 5  
----------------------------------------------------
                            ___                     
                     -2 + \/ 5
−27−35+1+107−35−2+5\frac{- \sqrt{2} \sqrt{7 - 3 \sqrt{5}} + 1 + \sqrt{10} \sqrt{7 - 3 \sqrt{5}}}{-2 + \sqrt{5}} 
(1 + sqrt(10)*sqrt(7 - 3*sqrt(5)) - sqrt(2)*sqrt(7 - 3*sqrt(5)))/(-2 + sqrt(5))
Potencias [src] 
                                   ______________
   ______________                 /          ___ 
  /          ___        1       \/  14 - 6*\/ 5  
\/  14 - 6*\/ 5   - --------- - -----------------
                          ___             ___    
                    2 - \/ 5        2 - \/ 5
14−65−14−652−5−12−5\sqrt{14 - 6 \sqrt{5}} - \frac{\sqrt{14 - 6 \sqrt{5}}}{2 - \sqrt{5}} - \frac{1}{2 - \sqrt{5}} 
sqrt(14 - 6*sqrt(5)) - 1/(2 - sqrt(5)) - sqrt(14 - 6*sqrt(5))/(2 - sqrt(5))
Denominador común [src] 
              _____________            _____________
      ____   /         ___      ___   /         ___ 
1 + \/ 10 *\/  7 - 3*\/ 5   - \/ 2 *\/  7 - 3*\/ 5  
----------------------------------------------------
                            ___                     
                     -2 + \/ 5
−27−35+1+107−35−2+5\frac{- \sqrt{2} \sqrt{7 - 3 \sqrt{5}} + 1 + \sqrt{10} \sqrt{7 - 3 \sqrt{5}}}{-2 + \sqrt{5}} 
(1 + sqrt(10)*sqrt(7 - 3*sqrt(5)) - sqrt(2)*sqrt(7 - 3*sqrt(5)))/(-2 + sqrt(5))
Unión de expresiones racionales [src] 
              _____________            
       ___   /         ___  /      ___\
-1 + \/ 2 *\/  7 - 3*\/ 5  *\1 - \/ 5 /
---------------------------------------
                     ___               
               2 - \/ 5
−1+2(1−5)7−352−5\frac{-1 + \sqrt{2} \left(1 - \sqrt{5}\right) \sqrt{7 - 3 \sqrt{5}}}{2 - \sqrt{5}} 
(-1 + sqrt(2)*sqrt(7 - 3*sqrt(5))*(1 - sqrt(5)))/(2 - sqrt(5))
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