Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
(sqrt((2x+1)^3)+sqrt((2x-1)^3))/(sqrt(4x+2sqrt(4x-1)))
¿Cómo vas a descomponer esta (sqrt((2x+1)^3)+sqrt((2x-1)^3))/(sqrt(4x+2sqrt(4x-1))) expresión en fracciones?
Solución
Ha introducido
[src]
____________ ____________
/ 3 / 3
\/ (2*x + 1) + \/ (2*x - 1)
---------------------------------
_____________________
/ _________
\/ 4*x + 2*\/ 4*x - 1
$$\frac{\sqrt{\left(2 x - 1\right)^{3}} + \sqrt{\left(2 x + 1\right)^{3}}}{\sqrt{4 x + 2 \sqrt{4 x - 1}}}$$
(sqrt((2*x + 1)^3) + sqrt((2*x - 1)^3))/sqrt(4*x + 2*sqrt(4*x - 1))
Simplificación general
[src]
/ ____________ _____________\
___ | / 3 / 3 |
\/ 2 *\\/ (1 + 2*x) + \/ (-1 + 2*x) /
------------------------------------------
____________________
/ __________
2*\/ \/ -1 + 4*x + 2*x
$$\frac{\sqrt{2} \left(\sqrt{\left(2 x - 1\right)^{3}} + \sqrt{\left(2 x + 1\right)^{3}}\right)}{2 \sqrt{2 x + \sqrt{4 x - 1}}}$$
sqrt(2)*(sqrt((1 + 2*x)^3) + sqrt((-1 + 2*x)^3))/(2*sqrt(sqrt(-1 + 4*x) + 2*x))
Respuesta numérica
[src]
0.5*(x + (-0.25 + x)^0.5)^(-0.5)*(2.82842712474619*((0.5 + x)^3)^0.5 + 2.82842712474619*((-0.5 + x)^3)^0.5)
0.5*(x + (-0.25 + x)^0.5)^(-0.5)*(2.82842712474619*((0.5 + x)^3)^0.5 + 2.82842712474619*((-0.5 + x)^3)^0.5)
Unión de expresiones racionales
[src]
/ ____________ _____________\
___ | / 3 / 3 |
\/ 2 *\\/ (1 + 2*x) + \/ (-1 + 2*x) /
------------------------------------------
____________________
/ __________
2*\/ \/ -1 + 4*x + 2*x
$$\frac{\sqrt{2} \left(\sqrt{\left(2 x - 1\right)^{3}} + \sqrt{\left(2 x + 1\right)^{3}}\right)}{2 \sqrt{2 x + \sqrt{4 x - 1}}}$$
sqrt(2)*(sqrt((1 + 2*x)^3) + sqrt((-1 + 2*x)^3))/(2*sqrt(sqrt(-1 + 4*x) + 2*x))
Combinatoria
[src]
/ ________________________ _________________________\
___ | / 3 2 / 2 3 |
\/ 2 *\\/ 1 + 6*x + 8*x + 12*x + \/ -1 - 12*x + 6*x + 8*x /
------------------------------------------------------------------
____________________
/ __________
2*\/ \/ -1 + 4*x + 2*x
$$\frac{\sqrt{2} \left(\sqrt{8 x^{3} - 12 x^{2} + 6 x - 1} + \sqrt{8 x^{3} + 12 x^{2} + 6 x + 1}\right)}{2 \sqrt{2 x + \sqrt{4 x - 1}}}$$
sqrt(2)*(sqrt(1 + 6*x + 8*x^3 + 12*x^2) + sqrt(-1 - 12*x^2 + 6*x + 8*x^3))/(2*sqrt(sqrt(-1 + 4*x) + 2*x))
Denominador racional
[src]
______________________ / ____________ _____________ ____________ _____________\
/ __________ | / 3 __________ / 3 __________ / 3 / 3 |
\/ 2*\/ -1 + 4*x + 4*x *\- \/ (1 + 2*x) *\/ -1 + 4*x - \/ (-1 + 2*x) *\/ -1 + 4*x + 2*x*\/ (1 + 2*x) + 2*x*\/ (-1 + 2*x) /
---------------------------------------------------------------------------------------------------------------------------------------
2
2 - 8*x + 8*x
$$\frac{\sqrt{4 x + 2 \sqrt{4 x - 1}} \left(2 x \sqrt{\left(2 x - 1\right)^{3}} + 2 x \sqrt{\left(2 x + 1\right)^{3}} - \sqrt{4 x - 1} \sqrt{\left(2 x - 1\right)^{3}} - \sqrt{4 x - 1} \sqrt{\left(2 x + 1\right)^{3}}\right)}{8 x^{2} - 8 x + 2}$$
sqrt(2*sqrt(-1 + 4*x) + 4*x)*(-sqrt((1 + 2*x)^3)*sqrt(-1 + 4*x) - sqrt((-1 + 2*x)^3)*sqrt(-1 + 4*x) + 2*x*sqrt((1 + 2*x)^3) + 2*x*sqrt((-1 + 2*x)^3))/(2 - 8*x + 8*x^2)
Denominador común
[src]
________________________ _________________________
___ / 3 2 ___ / 2 3
\/ 2 *\/ 1 + 6*x + 8*x + 12*x + \/ 2 *\/ -1 - 12*x + 6*x + 8*x
----------------------------------------------------------------------
____________________
/ __________
2*\/ \/ -1 + 4*x + 2*x
$$\frac{\sqrt{2} \sqrt{8 x^{3} - 12 x^{2} + 6 x - 1} + \sqrt{2} \sqrt{8 x^{3} + 12 x^{2} + 6 x + 1}}{2 \sqrt{2 x + \sqrt{4 x - 1}}}$$
(sqrt(2)*sqrt(1 + 6*x + 8*x^3 + 12*x^2) + sqrt(2)*sqrt(-1 - 12*x^2 + 6*x + 8*x^3))/(2*sqrt(sqrt(-1 + 4*x) + 2*x))