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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(5)/(sqrt(5)-sqrt(3)+1)-5*sqrt(15)-sqrt(5)-16/(7-2*sqrt(15))

¿Cómo vas a descomponer esta sqrt(5)/(sqrt(5)-sqrt(3)+1)-5*sqrt(15)-sqrt(5)-16/(7-2*sqrt(15)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
        ___                                        
      \/ 5              ____     ___        16     
----------------- - 5*\/ 15  - \/ 5  - ------------
  ___     ___                                  ____
\/ 5  - \/ 3  + 1                      7 - 2*\/ 15
((−515+5(−3+5)+1)−5)−167−215\left(\left(- 5 \sqrt{15} + \frac{\sqrt{5}}{\left(- \sqrt{3} + \sqrt{5}\right) + 1}\right) - \sqrt{5}\right) - \frac{16}{7 - 2 \sqrt{15}} 
sqrt(5)/(sqrt(5) - sqrt(3) + 1) - 5*sqrt(15) - sqrt(5) - 16/(7 - 2*sqrt(15))
Simplificación general [src] 
            ___        ____         ___
-69 - 239*\/ 5  + 18*\/ 15  + 309*\/ 3 
---------------------------------------
            ___       ____        ___  
  -7 - 13*\/ 5  + 2*\/ 15  + 17*\/ 3
−2395−69+1815+3093−135−7+215+173\frac{- 239 \sqrt{5} - 69 + 18 \sqrt{15} + 309 \sqrt{3}}{- 13 \sqrt{5} - 7 + 2 \sqrt{15} + 17 \sqrt{3}} 
(-69 - 239*sqrt(5) + 18*sqrt(15) + 309*sqrt(3))/(-7 - 13*sqrt(5) + 2*sqrt(15) + 17*sqrt(3))
Respuesta numérica [src] 
1.33442446948153
1.33442446948153
Potencias [src] 
                                            ___      
    ___        16            ____         \/ 5       
- \/ 5  - ------------ - 5*\/ 15  + -----------------
                  ____                    ___     ___
          7 - 2*\/ 15               1 + \/ 5  - \/ 3
−515−5+5−3+1+5−167−215- 5 \sqrt{15} - \sqrt{5} + \frac{\sqrt{5}}{- \sqrt{3} + 1 + \sqrt{5}} - \frac{16}{7 - 2 \sqrt{15}} 
-sqrt(5) - 16/(7 - 2*sqrt(15)) - 5*sqrt(15) + sqrt(5)/(1 + sqrt(5) - sqrt(3))
Denominador común [src] 
                    ___         ___    
         -6 - 122*\/ 5  + 156*\/ 3     
9 + -----------------------------------
              ___       ____        ___
    -7 - 13*\/ 5  + 2*\/ 15  + 17*\/ 3
−1225−6+1563−135−7+215+173+9\frac{- 122 \sqrt{5} - 6 + 156 \sqrt{3}}{- 13 \sqrt{5} - 7 + 2 \sqrt{15} + 17 \sqrt{3}} + 9 
9 + (-6 - 122*sqrt(5) + 156*sqrt(3))/(-7 - 13*sqrt(5) + 2*sqrt(15) + 17*sqrt(3))
Denominador racional [src] 
           ____       ___        ___
107 - 26*\/ 15  - 4*\/ 5  + 10*\/ 3 
------------------------------------
                 11
−2615−45+103+10711\frac{- 26 \sqrt{15} - 4 \sqrt{5} + 10 \sqrt{3} + 107}{11} 
(107 - 26*sqrt(15) - 4*sqrt(5) + 10*sqrt(3))/11
Parte trigonométrica [src] 
                                            ___      
    ___        16            ____         \/ 5       
- \/ 5  - ------------ - 5*\/ 15  + -----------------
                  ____                    ___     ___
          7 - 2*\/ 15               1 + \/ 5  - \/ 3
−515−5+5−3+1+5−167−215- 5 \sqrt{15} - \sqrt{5} + \frac{\sqrt{5}}{- \sqrt{3} + 1 + \sqrt{5}} - \frac{16}{7 - 2 \sqrt{15}} 
-sqrt(5) - 16/(7 - 2*sqrt(15)) - 5*sqrt(15) + sqrt(5)/(1 + sqrt(5) - sqrt(3))
Unión de expresiones racionales [src] 
           ___        ___   /        ____\ /  ___     ___ /      ___     ___\       ____ /      ___     ___\\
-16 - 16*\/ 5  + 16*\/ 3  + \7 - 2*\/ 15 /*\\/ 5  - \/ 5 *\1 + \/ 5  - \/ 3 / - 5*\/ 15 *\1 + \/ 5  - \/ 3 //
-------------------------------------------------------------------------------------------------------------
                                      /        ____\ /      ___     ___\                                     
                                      \7 - 2*\/ 15 /*\1 + \/ 5  - \/ 3 /
−165−16+(7−215)(−515(−3+1+5)−5(−3+1+5)+5)+163(7−215)(−3+1+5)\frac{- 16 \sqrt{5} - 16 + \left(7 - 2 \sqrt{15}\right) \left(- 5 \sqrt{15} \left(- \sqrt{3} + 1 + \sqrt{5}\right) - \sqrt{5} \left(- \sqrt{3} + 1 + \sqrt{5}\right) + \sqrt{5}\right) + 16 \sqrt{3}}{\left(7 - 2 \sqrt{15}\right) \left(- \sqrt{3} + 1 + \sqrt{5}\right)} 
(-16 - 16*sqrt(5) + 16*sqrt(3) + (7 - 2*sqrt(15))*(sqrt(5) - sqrt(5)*(1 + sqrt(5) - sqrt(3)) - 5*sqrt(15)*(1 + sqrt(5) - sqrt(3))))/((7 - 2*sqrt(15))*(1 + sqrt(5) - sqrt(3)))
Combinatoria [src] 
 /            ___        ____         ___\ 
-\-69 - 239*\/ 5  + 18*\/ 15  + 309*\/ 3 / 
-------------------------------------------
    /         ____\ /       ___     ___\   
    \-7 + 2*\/ 15 /*\-1 + \/ 3  - \/ 5 /
−−2395−69+1815+3093(−7+215)(−5−1+3)- \frac{- 239 \sqrt{5} - 69 + 18 \sqrt{15} + 309 \sqrt{3}}{\left(-7 + 2 \sqrt{15}\right) \left(- \sqrt{5} - 1 + \sqrt{3}\right)} 
-(-69 - 239*sqrt(5) + 18*sqrt(15) + 309*sqrt(3))/((-7 + 2*sqrt(15))*(-1 + sqrt(3) - sqrt(5)))
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