Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
(a*sqrt(a)+b*sqrt(b)/sqrt(a)+sqrt(b))/(a-b)+2*sqrt(b)/sqrt(a)+sqrt(b)
¿Cómo vas a descomponer esta (a*sqrt(a)+b*sqrt(b)/sqrt(a)+sqrt(b))/(a-b)+2*sqrt(b)/sqrt(a)+sqrt(b) expresión en fracciones?
Solución
Ha introducido
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___
___ b*\/ b ___
a*\/ a + ------- + \/ b
___ ___
\/ a 2*\/ b ___
------------------------- + ------- + \/ b
a - b ___
\/ a
$$\sqrt{b} + \left(\frac{\sqrt{b} + \left(\sqrt{a} a + \frac{\sqrt{b} b}{\sqrt{a}}\right)}{a - b} + \frac{2 \sqrt{b}}{\sqrt{a}}\right)$$
(a*sqrt(a) + (b*sqrt(b))/sqrt(a) + sqrt(b))/(a - b) + (2*sqrt(b))/sqrt(a) + sqrt(b)
Simplificación general
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___ / 2 3/2 ___ ___\ ___ ___ ___
\/ a *\a + b + \/ a *\/ b / + a*\/ b *(a - b) + 2*\/ a *\/ b *(a - b)
-------------------------------------------------------------------------
a*(a - b)
$$\frac{2 \sqrt{a} \sqrt{b} \left(a - b\right) + \sqrt{a} \left(\sqrt{a} \sqrt{b} + a^{2} + b^{\frac{3}{2}}\right) + a \sqrt{b} \left(a - b\right)}{a \left(a - b\right)}$$
(sqrt(a)*(a^2 + b^(3/2) + sqrt(a)*sqrt(b)) + a*sqrt(b)*(a - b) + 2*sqrt(a)*sqrt(b)*(a - b))/(a*(a - b))
Respuesta numérica
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b^0.5 + (a^1.5 + b^0.5 + a^(-0.5)*b^1.5)/(a - b) + 2.0*a^(-0.5)*b^0.5
b^0.5 + (a^1.5 + b^0.5 + a^(-0.5)*b^1.5)/(a - b) + 2.0*a^(-0.5)*b^0.5
Compilar la expresión
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3/2
3/2 ___ b
a + \/ b + -----
___
___ / 2 \ \/ a
\/ b *|1 + -----| + --------------------
| ___| a - b
\ \/ a /
$$\sqrt{b} \left(1 + \frac{2}{\sqrt{a}}\right) + \frac{a^{\frac{3}{2}} + \sqrt{b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}}}{a - b}$$
3/2
3/2 ___ b
a + \/ b + -----
___ ___
___ \/ a 2*\/ b
\/ b + -------------------- + -------
a - b ___
\/ a
$$\sqrt{b} + \frac{a^{\frac{3}{2}} + \sqrt{b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}}}{a - b} + \frac{2 \sqrt{b}}{\sqrt{a}}$$
sqrt(b) + (a^(3/2) + sqrt(b) + b^(3/2)/sqrt(a))/(a - b) + 2*sqrt(b)/sqrt(a)
Potencias
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3/2
3/2 ___ b
a + \/ b + -----
___ ___
___ \/ a 2*\/ b
\/ b + -------------------- + -------
a - b ___
\/ a
$$\sqrt{b} + \frac{a^{\frac{3}{2}} + \sqrt{b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}}}{a - b} + \frac{2 \sqrt{b}}{\sqrt{a}}$$
sqrt(b) + (a^(3/2) + sqrt(b) + b^(3/2)/sqrt(a))/(a - b) + 2*sqrt(b)/sqrt(a)
Unión de expresiones racionales
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2 3/2 ___ ___ ___ ___ ___
a + b + \/ a *\/ b + 2*\/ b *(a - b) + \/ a *\/ b *(a - b)
---------------------------------------------------------------
___
\/ a *(a - b)
$$\frac{\sqrt{a} \sqrt{b} \left(a - b\right) + \sqrt{a} \sqrt{b} + a^{2} + b^{\frac{3}{2}} + 2 \sqrt{b} \left(a - b\right)}{\sqrt{a} \left(a - b\right)}$$
(a^2 + b^(3/2) + sqrt(a)*sqrt(b) + 2*sqrt(b)*(a - b) + sqrt(a)*sqrt(b)*(a - b))/(sqrt(a)*(a - b))
Parte trigonométrica
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3/2
3/2 ___ b
a + \/ b + -----
___ ___
___ \/ a 2*\/ b
\/ b + -------------------- + -------
a - b ___
\/ a
$$\sqrt{b} + \frac{a^{\frac{3}{2}} + \sqrt{b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}}}{a - b} + \frac{2 \sqrt{b}}{\sqrt{a}}$$
sqrt(b) + (a^(3/2) + sqrt(b) + b^(3/2)/sqrt(a))/(a - b) + 2*sqrt(b)/sqrt(a)
Denominador racional
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___ / 2 3/2 ___ ___\ ___ ___ ___
\/ a *\a + b + \/ a *\/ b / + a*\/ b *(a - b) + 2*\/ a *\/ b *(a - b)
-------------------------------------------------------------------------
a*(a - b)
$$\frac{2 \sqrt{a} \sqrt{b} \left(a - b\right) + \sqrt{a} \left(\sqrt{a} \sqrt{b} + a^{2} + b^{\frac{3}{2}}\right) + a \sqrt{b} \left(a - b\right)}{a \left(a - b\right)}$$
(sqrt(a)*(a^2 + b^(3/2) + sqrt(a)*sqrt(b)) + a*sqrt(b)*(a - b) + 2*sqrt(a)*sqrt(b)*(a - b))/(a*(a - b))
Denominador común
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5/2 ___ ___ 3/2 3/2 ___
___ a + a*\/ b - \/ a *b + 2*a *\/ b
\/ b + ------------------------------------------
2
a - a*b
$$\sqrt{b} + \frac{a^{\frac{5}{2}} + 2 a^{\frac{3}{2}} \sqrt{b} - \sqrt{a} b^{\frac{3}{2}} + a \sqrt{b}}{a^{2} - a b}$$
sqrt(b) + (a^(5/2) + a*sqrt(b) - sqrt(a)*b^(3/2) + 2*a^(3/2)*sqrt(b))/(a^2 - a*b)
Combinatoria
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2 3/2 ___ ___ 3/2 ___ ___ 3/2 ___
a - b + \/ a *\/ b + a *\/ b - \/ a *b + 2*a*\/ b
-------------------------------------------------------------
___
\/ a *(a - b)
$$\frac{a^{\frac{3}{2}} \sqrt{b} - \sqrt{a} b^{\frac{3}{2}} + \sqrt{a} \sqrt{b} + a^{2} + 2 a \sqrt{b} - b^{\frac{3}{2}}}{\sqrt{a} \left(a - b\right)}$$
(a^2 - b^(3/2) + sqrt(a)*sqrt(b) + a^(3/2)*sqrt(b) - sqrt(a)*b^(3/2) + 2*a*sqrt(b))/(sqrt(a)*(a - b))