Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(3+x^3)*(sqrt(2+x^2)+x*(1+x)/sqrt(2+x^2))+3*x^2*sqrt(2+x^2)*(1+x)/(2*sqrt(3+x^3))
¿Cómo vas a descomponer esta sqrt(3+x^3)*(sqrt(2+x^2)+x*(1+x)/sqrt(2+x^2))+3*x^2*sqrt(2+x^2)*(1+x)/(2*sqrt(3+x^3)) expresión en fracciones?
Solución
Ha introducido
[src]
________
________ / ________ \ 2 / 2
/ 3 | / 2 x*(1 + x) | 3*x *\/ 2 + x *(1 + x)
\/ 3 + x *|\/ 2 + x + -----------| + ------------------------
| ________| ________
| / 2 | / 3
\ \/ 2 + x / 2*\/ 3 + x
$$\frac{3 x^{2} \sqrt{x^{2} + 2} \left(x + 1\right)}{2 \sqrt{x^{3} + 3}} + \sqrt{x^{3} + 3} \left(\frac{x \left(x + 1\right)}{\sqrt{x^{2} + 2}} + \sqrt{x^{2} + 2}\right)$$
sqrt(3 + x^3)*(sqrt(2 + x^2) + (x*(1 + x))/sqrt(2 + x^2)) + (((3*x^2)*sqrt(2 + x^2))*(1 + x))/((2*sqrt(3 + x^3)))
Simplificación general
[src]
4 5 3 2
12 + 5*x + 6*x + 7*x + 10*x + 18*x
--------------------------------------
________ ________
/ 2 / 3
2*\/ 2 + x *\/ 3 + x
$$\frac{7 x^{5} + 5 x^{4} + 10 x^{3} + 18 x^{2} + 6 x + 12}{2 \sqrt{x^{2} + 2} \sqrt{x^{3} + 3}}$$
(12 + 5*x^4 + 6*x + 7*x^5 + 10*x^3 + 18*x^2)/(2*sqrt(2 + x^2)*sqrt(3 + x^3))
Potencias
[src]
________
2 / 2 /3 3*x\
________ / ________ \ x *\/ 2 + x *|- + ---|
/ 3 | / 2 x*(1 + x) | \2 2 /
\/ 3 + x *|\/ 2 + x + -----------| + ------------------------
| ________| ________
| / 2 | / 3
\ \/ 2 + x / \/ 3 + x
$$\frac{x^{2} \left(\frac{3 x}{2} + \frac{3}{2}\right) \sqrt{x^{2} + 2}}{\sqrt{x^{3} + 3}} + \sqrt{x^{3} + 3} \left(\frac{x \left(x + 1\right)}{\sqrt{x^{2} + 2}} + \sqrt{x^{2} + 2}\right)$$
________
________ / ________ \ 2 / 2
/ 3 | / 2 x*(1 + x) | 3*x *\/ 2 + x *(1 + x)
\/ 3 + x *|\/ 2 + x + -----------| + ------------------------
| ________| ________
| / 2 | / 3
\ \/ 2 + x / 2*\/ 3 + x
$$\frac{3 x^{2} \left(x + 1\right) \sqrt{x^{2} + 2}}{2 \sqrt{x^{3} + 3}} + \sqrt{x^{3} + 3} \left(\frac{x \left(x + 1\right)}{\sqrt{x^{2} + 2}} + \sqrt{x^{2} + 2}\right)$$
sqrt(3 + x^3)*(sqrt(2 + x^2) + x*(1 + x)/sqrt(2 + x^2)) + 3*x^2*sqrt(2 + x^2)*(1 + x)/(2*sqrt(3 + x^3))
Respuesta numérica
[src]
1.73205080756888*(1 + 0.333333333333333*x^3)^0.5*(1.4142135623731*(1 + 0.5*x^2)^0.5 + 0.707106781186547*x*(1 + 0.5*x^2)^(-0.5)*(1.0 + x)) + 1.22474487139159*x^2*(1 + 0.5*x^2)^0.5*(1 + 0.333333333333333*x^3)^(-0.5)*(1.0 + x)
1.73205080756888*(1 + 0.333333333333333*x^3)^0.5*(1.4142135623731*(1 + 0.5*x^2)^0.5 + 0.707106781186547*x*(1 + 0.5*x^2)^(-0.5)*(1.0 + x)) + 1.22474487139159*x^2*(1 + 0.5*x^2)^0.5*(1 + 0.333333333333333*x^3)^(-0.5)*(1.0 + x)
Unión de expresiones racionales
[src]
/ 3\ / 2 \ 2 / 2\
2*\3 + x /*\2 + x + x*(1 + x)/ + 3*x *(1 + x)*\2 + x /
-------------------------------------------------------
________ ________
/ 2 / 3
2*\/ 2 + x *\/ 3 + x
$$\frac{3 x^{2} \left(x + 1\right) \left(x^{2} + 2\right) + 2 \left(x^{3} + 3\right) \left(x^{2} + x \left(x + 1\right) + 2\right)}{2 \sqrt{x^{2} + 2} \sqrt{x^{3} + 3}}$$
(2*(3 + x^3)*(2 + x^2 + x*(1 + x)) + 3*x^2*(1 + x)*(2 + x^2))/(2*sqrt(2 + x^2)*sqrt(3 + x^3))
Denominador racional
[src]
________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________
/ 2 / 3 4 / 2 / 3 / 2 / 3 5 / 2 / 3 3 / 2 / 3 2 / 2 / 3
12*\/ 2 + x *\/ 3 + x + 5*x *\/ 2 + x *\/ 3 + x + 6*x*\/ 2 + x *\/ 3 + x + 7*x *\/ 2 + x *\/ 3 + x + 10*x *\/ 2 + x *\/ 3 + x + 18*x *\/ 2 + x *\/ 3 + x
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\ / 3\
2*\2 + x /*\3 + x /
$$\frac{7 x^{5} \sqrt{x^{2} + 2} \sqrt{x^{3} + 3} + 5 x^{4} \sqrt{x^{2} + 2} \sqrt{x^{3} + 3} + 10 x^{3} \sqrt{x^{2} + 2} \sqrt{x^{3} + 3} + 18 x^{2} \sqrt{x^{2} + 2} \sqrt{x^{3} + 3} + 6 x \sqrt{x^{2} + 2} \sqrt{x^{3} + 3} + 12 \sqrt{x^{2} + 2} \sqrt{x^{3} + 3}}{2 \left(x^{2} + 2\right) \left(x^{3} + 3\right)}$$
(12*sqrt(2 + x^2)*sqrt(3 + x^3) + 5*x^4*sqrt(2 + x^2)*sqrt(3 + x^3) + 6*x*sqrt(2 + x^2)*sqrt(3 + x^3) + 7*x^5*sqrt(2 + x^2)*sqrt(3 + x^3) + 10*x^3*sqrt(2 + x^2)*sqrt(3 + x^3) + 18*x^2*sqrt(2 + x^2)*sqrt(3 + x^3))/(2*(2 + x^2)*(3 + x^3))
Denominador común
[src]
4 5 3 2
12 + 5*x + 6*x + 7*x + 10*x + 18*x
--------------------------------------
________ ________
/ 2 / 3
2*\/ 2 + x *\/ 3 + x
$$\frac{7 x^{5} + 5 x^{4} + 10 x^{3} + 18 x^{2} + 6 x + 12}{2 \sqrt{x^{2} + 2} \sqrt{x^{3} + 3}}$$
(12 + 5*x^4 + 6*x + 7*x^5 + 10*x^3 + 18*x^2)/(2*sqrt(2 + x^2)*sqrt(3 + x^3))
Parte trigonométrica
[src]
________
________ / ________ \ 2 / 2
/ 3 | / 2 x*(1 + x) | 3*x *\/ 2 + x *(1 + x)
\/ 3 + x *|\/ 2 + x + -----------| + ------------------------
| ________| ________
| / 2 | / 3
\ \/ 2 + x / 2*\/ 3 + x
$$\frac{3 x^{2} \left(x + 1\right) \sqrt{x^{2} + 2}}{2 \sqrt{x^{3} + 3}} + \sqrt{x^{3} + 3} \left(\frac{x \left(x + 1\right)}{\sqrt{x^{2} + 2}} + \sqrt{x^{2} + 2}\right)$$
sqrt(3 + x^3)*(sqrt(2 + x^2) + x*(1 + x)/sqrt(2 + x^2)) + 3*x^2*sqrt(2 + x^2)*(1 + x)/(2*sqrt(3 + x^3))
Combinatoria
[src]
4 5 3 2
12 + 5*x + 6*x + 7*x + 10*x + 18*x
--------------------------------------
________ ________
/ 2 / 3
2*\/ 2 + x *\/ 3 + x
$$\frac{7 x^{5} + 5 x^{4} + 10 x^{3} + 18 x^{2} + 6 x + 12}{2 \sqrt{x^{2} + 2} \sqrt{x^{3} + 3}}$$
(12 + 5*x^4 + 6*x + 7*x^5 + 10*x^3 + 18*x^2)/(2*sqrt(2 + x^2)*sqrt(3 + x^3))
Compilar la expresión
[src]
________
________ / ________ \ 2 / 2
/ 3 | / 2 x*(1 + x) | 3*x *\/ 2 + x *(1 + x)
\/ 3 + x *|\/ 2 + x + -----------| + ------------------------
| ________| ________
| / 2 | / 3
\ \/ 2 + x / 2*\/ 3 + x
$$\frac{3 x^{2} \left(x + 1\right) \sqrt{x^{2} + 2}}{2 \sqrt{x^{3} + 3}} + \sqrt{x^{3} + 3} \left(\frac{x \left(x + 1\right)}{\sqrt{x^{2} + 2}} + \sqrt{x^{2} + 2}\right)$$
sqrt(3 + x^3)*(sqrt(2 + x^2) + x*(1 + x)/sqrt(2 + x^2)) + 3*x^2*sqrt(2 + x^2)*(1 + x)/(2*sqrt(3 + x^3))