Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(1+x)*(-2/15+6*x^2/5+16*x/15)+(3*x^3+4*x^2-x-2)/(15*sqrt(1+x))
¿Cómo vas a descomponer esta sqrt(1+x)*(-2/15+6*x^2/5+16*x/15)+(3*x^3+4*x^2-x-2)/(15*sqrt(1+x)) expresión en fracciones?
Solución
Ha introducido
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/ 2 \ 3 2
_______ | 2 6*x 16*x| 3*x + 4*x - x - 2
\/ 1 + x *|- -- + ---- + ----| + -------------------
\ 15 5 15 / _______
15*\/ 1 + x
$$\sqrt{x + 1} \left(\frac{16 x}{15} + \left(\frac{6 x^{2}}{5} - \frac{2}{15}\right)\right) + \frac{\left(- x + \left(3 x^{3} + 4 x^{2}\right)\right) - 2}{15 \sqrt{x + 1}}$$
sqrt(1 + x)*(-2/15 + (6*x^2)/5 + (16*x)/15) + (3*x^3 + 4*x^2 - x - 2)/((15*sqrt(1 + x)))
Simplificación general
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3 2
-4 + 13*x + 21*x + 38*x
-------------------------
_______
15*\/ 1 + x
$$\frac{21 x^{3} + 38 x^{2} + 13 x - 4}{15 \sqrt{x + 1}}$$
(-4 + 13*x + 21*x^3 + 38*x^2)/(15*sqrt(1 + x))
Respuesta numérica
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(1.0 + x)^0.5*(-0.133333333333333 + 1.2*x^2 + 1.06666666666667*x) + 0.0666666666666667*(1.0 + x)^(-0.5)*(-2.0 - x + 4.0*x^2 + 3.0*x^3)
(1.0 + x)^0.5*(-0.133333333333333 + 1.2*x^2 + 1.06666666666667*x) + 0.0666666666666667*(1.0 + x)^(-0.5)*(-2.0 - x + 4.0*x^2 + 3.0*x^3)
Unión de expresiones racionales
[src]
/ 2\
-2 + x*(-1 + x*(4 + 3*x)) + 2*(1 + x)*\-1 + 8*x + 9*x /
-------------------------------------------------------
_______
15*\/ 1 + x
$$\frac{x \left(x \left(3 x + 4\right) - 1\right) + 2 \left(x + 1\right) \left(9 x^{2} + 8 x - 1\right) - 2}{15 \sqrt{x + 1}}$$
(-2 + x*(-1 + x*(4 + 3*x)) + 2*(1 + x)*(-1 + 8*x + 9*x^2))/(15*sqrt(1 + x))
Denominador racional
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_______ _______ 3 _______ 2 _______
- 4500*\/ 1 + x + 14625*x*\/ 1 + x + 23625*x *\/ 1 + x + 42750*x *\/ 1 + x
------------------------------------------------------------------------------
16875 + 16875*x
$$\frac{23625 x^{3} \sqrt{x + 1} + 42750 x^{2} \sqrt{x + 1} + 14625 x \sqrt{x + 1} - 4500 \sqrt{x + 1}}{16875 x + 16875}$$
(-4500*sqrt(1 + x) + 14625*x*sqrt(1 + x) + 23625*x^3*sqrt(1 + x) + 42750*x^2*sqrt(1 + x))/(16875 + 16875*x)
Compilar la expresión
[src]
/ 2 \ 3 2
_______ | 2 6*x 16*x| -2 - x + 3*x + 4*x
\/ 1 + x *|- -- + ---- + ----| + --------------------
\ 15 5 15 / _______
15*\/ 1 + x
$$\sqrt{x + 1} \left(\frac{6 x^{2}}{5} + \frac{16 x}{15} - \frac{2}{15}\right) + \frac{3 x^{3} + 4 x^{2} - x - 2}{15 \sqrt{x + 1}}$$
sqrt(1 + x)*(-2/15 + 6*x^2/5 + 16*x/15) + (-2 - x + 3*x^3 + 4*x^2)/(15*sqrt(1 + x))
Parte trigonométrica
[src]
/ 2 \ 3 2
_______ | 2 6*x 16*x| -2 - x + 3*x + 4*x
\/ 1 + x *|- -- + ---- + ----| + --------------------
\ 15 5 15 / _______
15*\/ 1 + x
$$\sqrt{x + 1} \left(\frac{6 x^{2}}{5} + \frac{16 x}{15} - \frac{2}{15}\right) + \frac{3 x^{3} + 4 x^{2} - x - 2}{15 \sqrt{x + 1}}$$
sqrt(1 + x)*(-2/15 + 6*x^2/5 + 16*x/15) + (-2 - x + 3*x^3 + 4*x^2)/(15*sqrt(1 + x))
Potencias
[src]
/ 2 \ 3 2
_______ | 2 6*x 16*x| -2 - x + 3*x + 4*x
\/ 1 + x *|- -- + ---- + ----| + --------------------
\ 15 5 15 / _______
15*\/ 1 + x
$$\sqrt{x + 1} \left(\frac{6 x^{2}}{5} + \frac{16 x}{15} - \frac{2}{15}\right) + \frac{3 x^{3} + 4 x^{2} - x - 2}{15 \sqrt{x + 1}}$$
3 2
2 x x 4*x
/ 2 \ - -- - -- + -- + ----
_______ | 2 6*x 16*x| 15 15 5 15
\/ 1 + x *|- -- + ---- + ----| + ---------------------
\ 15 5 15 / _______
\/ 1 + x
$$\sqrt{x + 1} \left(\frac{6 x^{2}}{5} + \frac{16 x}{15} - \frac{2}{15}\right) + \frac{\frac{x^{3}}{5} + \frac{4 x^{2}}{15} - \frac{x}{15} - \frac{2}{15}}{\sqrt{x + 1}}$$
sqrt(1 + x)*(-2/15 + 6*x^2/5 + 16*x/15) + (-2/15 - x/15 + x^3/5 + 4*x^2/15)/sqrt(1 + x)
Combinatoria
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3/2
(1 + x) *(-4 + 21*x)
----------------------
15
$$\frac{\left(x + 1\right)^{\frac{3}{2}} \left(21 x - 4\right)}{15}$$
(1 + x)^(3/2)*(-4 + 21*x)/15
Denominador común
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3 2
-4 + 13*x + 21*x + 38*x
-------------------------
_______
15*\/ 1 + x
$$\frac{21 x^{3} + 38 x^{2} + 13 x - 4}{15 \sqrt{x + 1}}$$
(-4 + 13*x + 21*x^3 + 38*x^2)/(15*sqrt(1 + x))