Sr Examen
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?
Solución
Ha introducido
[src]
___
\/ 5 ____ ___ 16
----------------- - 5*\/ 15 - \/ 5 - ------------
___ ___ ____
\/ 5 - \/ 3 + 1 7 - 2*\/ 15
$$\left(\left(- 5 \sqrt{15} + \frac{\sqrt{5}}{\left(- \sqrt{3} + \sqrt{5}\right) + 1}\right) - \sqrt{5}\right) - \frac{16}{7 - 2 \sqrt{15}}$$
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
$$\frac{- 239 \sqrt{5} - 69 + 18 \sqrt{15} + 309 \sqrt{3}}{- 13 \sqrt{5} - 7 + 2 \sqrt{15} + 17 \sqrt{3}}$$
(-69 - 239*sqrt(5) + 18*sqrt(15) + 309*sqrt(3))/(-7 - 13*sqrt(5) + 2*sqrt(15) + 17*sqrt(3))
Potencias
[src]
___
___ 16 ____ \/ 5
- \/ 5 - ------------ - 5*\/ 15 + -----------------
____ ___ ___
7 - 2*\/ 15 1 + \/ 5 - \/ 3
$$- 5 \sqrt{15} - \sqrt{5} + \frac{\sqrt{5}}{- \sqrt{3} + 1 + \sqrt{5}} - \frac{16}{7 - 2 \sqrt{15}}$$
-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
$$\frac{- 122 \sqrt{5} - 6 + 156 \sqrt{3}}{- 13 \sqrt{5} - 7 + 2 \sqrt{15} + 17 \sqrt{3}} + 9$$
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
$$\frac{- 26 \sqrt{15} - 4 \sqrt{5} + 10 \sqrt{3} + 107}{11}$$
(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
$$- 5 \sqrt{15} - \sqrt{5} + \frac{\sqrt{5}}{- \sqrt{3} + 1 + \sqrt{5}} - \frac{16}{7 - 2 \sqrt{15}}$$
-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 /
$$\frac{- 16 \sqrt{5} - 16 + \left(7 - 2 \sqrt{15}\right) \left(- 5 \sqrt{15} \left(- \sqrt{3} + 1 + \sqrt{5}\right) - \sqrt{5} \left(- \sqrt{3} + 1 + \sqrt{5}\right) + \sqrt{5}\right) + 16 \sqrt{3}}{\left(7 - 2 \sqrt{15}\right) \left(- \sqrt{3} + 1 + \sqrt{5}\right)}$$
(-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 /
$$- \frac{- 239 \sqrt{5} - 69 + 18 \sqrt{15} + 309 \sqrt{3}}{\left(-7 + 2 \sqrt{15}\right) \left(- \sqrt{5} - 1 + \sqrt{3}\right)}$$
-(-69 - 239*sqrt(5) + 18*sqrt(15) + 309*sqrt(3))/((-7 + 2*sqrt(15))*(-1 + sqrt(3) - sqrt(5)))