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