Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(a)-(a-1/a^2)/(sqrt(a)-1/sqrt(a))+(1-1/a^2)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2)
¿Cómo vas a descomponer esta sqrt(a)-(a-1/a^2)/(sqrt(a)-1/sqrt(a))+(1-1/a^2)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2) expresión en fracciones?
Solución
Ha introducido
[src]
1 1
a - -- 1 - --
2 2
___ a a 2
\/ a - ------------- + ------------- + ----
___ 1 ___ 1 3/2
\/ a - ----- \/ a + ----- a
___ ___
\/ a \/ a
$$\left(\frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} + \left(\sqrt{a} - \frac{a - \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}}\right)\right) + \frac{2}{a^{\frac{3}{2}}}$$
sqrt(a) - (a - 1/a^2)/(sqrt(a) - 1/sqrt(a)) + (1 - 1/a^2)/(sqrt(a) + 1/(sqrt(a))) + 2/a^(3/2)
Potencias
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1 1
1 - -- a - --
2 2
___ 2 a a
\/ a + ---- + ------------- - -------------
3/2 ___ 1 ___ 1
a \/ a + ----- \/ a - -----
___ ___
\/ a \/ a
$$\sqrt{a} + \frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} - \frac{a - \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}} + \frac{2}{a^{\frac{3}{2}}}$$
1 1
1 - -- -- - a
2 2
___ 2 a a
\/ a + ---- + ------------- + -------------
3/2 ___ 1 ___ 1
a \/ a + ----- \/ a - -----
___ ___
\/ a \/ a
$$\sqrt{a} + \frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} + \frac{- a + \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}} + \frac{2}{a^{\frac{3}{2}}}$$
sqrt(a) + 2/a^(3/2) + (1 - 1/a^2)/(sqrt(a) + 1/sqrt(a)) + (a^(-2) - a)/(sqrt(a) - 1/sqrt(a))
Denominador racional
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0 -------------------- 11 a *(1 + a)*(-1 + a)
$$\frac{0}{a^{11} \left(a - 1\right) \left(a + 1\right)}$$
0/(a^11*(1 + a)*(-1 + a))
Respuesta numérica
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a^0.5 + 2.0*a^(-1.5) + (1.0 - 1/a^2)/(a^0.5 + a^(-0.5)) - (a - 1/a^2)/(a^0.5 - a^(-0.5))
a^0.5 + 2.0*a^(-1.5) + (1.0 - 1/a^2)/(a^0.5 + a^(-0.5)) - (a - 1/a^2)/(a^0.5 - a^(-0.5))
Unión de expresiones racionales
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/ 3 2 \ / 2\
(1 + a)*\1 - a + a *(-1 + a)/ + (-1 + a)*\-1 + a / + 2*(1 + a)*(-1 + a)
------------------------------------------------------------------------
3/2
a *(1 + a)*(-1 + a)
$$\frac{2 \left(a - 1\right) \left(a + 1\right) + \left(a - 1\right) \left(a^{2} - 1\right) + \left(a + 1\right) \left(- a^{3} + a^{2} \left(a - 1\right) + 1\right)}{a^{\frac{3}{2}} \left(a - 1\right) \left(a + 1\right)}$$
((1 + a)*(1 - a^3 + a^2*(-1 + a)) + (-1 + a)*(-1 + a^2) + 2*(1 + a)*(-1 + a))/(a^(3/2)*(1 + a)*(-1 + a))
Parte trigonométrica
[src]
1 1
1 - -- a - --
2 2
___ 2 a a
\/ a + ---- + ------------- - -------------
3/2 ___ 1 ___ 1
a \/ a + ----- \/ a - -----
___ ___
\/ a \/ a
$$\sqrt{a} + \frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} - \frac{a - \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}} + \frac{2}{a^{\frac{3}{2}}}$$
sqrt(a) + 2/a^(3/2) + (1 - 1/a^2)/(sqrt(a) + 1/sqrt(a)) - (a - 1/a^2)/(sqrt(a) - 1/sqrt(a))
Compilar la expresión
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1 1
1 - -- a - --
2 2
___ 2 a a
\/ a + ---- + ------------- - -------------
3/2 ___ 1 ___ 1
a \/ a + ----- \/ a - -----
___ ___
\/ a \/ a
$$\sqrt{a} + \frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} - \frac{a - \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}} + \frac{2}{a^{\frac{3}{2}}}$$
sqrt(a) + 2/a^(3/2) + (1 - 1/a^2)/(sqrt(a) + 1/sqrt(a)) - (a - 1/a^2)/(sqrt(a) - 1/sqrt(a))