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
[src]
___ ___ ___
___ b*\/ b \/ b 2*\/ b ___
a*\/ a + ------- + ----- + ------- + \/ b
___ a - b ___
\/ a \/ a
$$\sqrt{b} + \left(\left(\frac{\sqrt{b}}{a - b} + \left(\sqrt{a} a + \frac{\sqrt{b} b}{\sqrt{a}}\right)\right) + \frac{2 \sqrt{b}}{\sqrt{a}}\right)$$
a*sqrt(a) + (b*sqrt(b))/sqrt(a) + sqrt(b)/(a - b) + (2*sqrt(b))/sqrt(a) + sqrt(b)
Simplificación general
[src]
___ ___ ___ / 3/2 ___\ ___
\/ a *\/ b + \/ a *(a - b)*\a + \/ b / + \/ b *(2 + b)*(a - b)
------------------------------------------------------------------
___
\/ a *(a - b)
$$\frac{\sqrt{a} \sqrt{b} + \sqrt{a} \left(a - b\right) \left(a^{\frac{3}{2}} + \sqrt{b}\right) + \sqrt{b} \left(a - b\right) \left(b + 2\right)}{\sqrt{a} \left(a - b\right)}$$
(sqrt(a)*sqrt(b) + sqrt(a)*(a - b)*(a^(3/2) + sqrt(b)) + sqrt(b)*(2 + b)*(a - b))/(sqrt(a)*(a - b))
Respuesta numérica
[src]
a^1.5 + b^0.5 + a^(-0.5)*b^1.5 + b^0.5/(a - b) + 2.0*a^(-0.5)*b^0.5
a^1.5 + b^0.5 + a^(-0.5)*b^1.5 + b^0.5/(a - b) + 2.0*a^(-0.5)*b^0.5
Denominador común
[src]
/ 3 5/2 3/2 3/2 ___ ___ 3/2 ___ 2 ___ 3/2 ___\
-\a - b - 2*b + a*b + \/ a *\/ b + a *\/ b - b*a - \/ a *b + 2*a*\/ b /
------------------------------------------------------------------------------------------
3/2 ___
- a + b*\/ a
$$- \frac{a^{\frac{3}{2}} \sqrt{b} - \sqrt{a} b^{\frac{3}{2}} + \sqrt{a} \sqrt{b} + a^{3} - a^{2} b + a b^{\frac{3}{2}} + 2 a \sqrt{b} - b^{\frac{5}{2}} - 2 b^{\frac{3}{2}}}{- a^{\frac{3}{2}} + \sqrt{a} b}$$
-(a^3 - b^(5/2) - 2*b^(3/2) + a*b^(3/2) + sqrt(a)*sqrt(b) + a^(3/2)*sqrt(b) - b*a^2 - sqrt(a)*b^(3/2) + 2*a*sqrt(b))/(-a^(3/2) + b*sqrt(a))
Compilar la expresión
[src]
3/2
3/2 b ___ / 1 2 \
a + ----- + \/ b *|1 + ----- + -----|
___ | a - b ___|
\/ a \ \/ a /
$$a^{\frac{3}{2}} + \sqrt{b} \left(1 + \frac{1}{a - b} + \frac{2}{\sqrt{a}}\right) + \frac{b^{\frac{3}{2}}}{\sqrt{a}}$$
3/2 ___ ___
3/2 ___ b \/ b 2*\/ b
a + \/ b + ----- + ----- + -------
___ a - b ___
\/ a \/ a
$$a^{\frac{3}{2}} + \sqrt{b} + \frac{\sqrt{b}}{a - b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}} + \frac{2 \sqrt{b}}{\sqrt{a}}$$
3/2 ___ ___
3/2 ___ b + 2*\/ b \/ b
a + \/ b + -------------- + -----
___ a - b
\/ a
$$a^{\frac{3}{2}} + \sqrt{b} + \frac{\sqrt{b}}{a - b} + \frac{b^{\frac{3}{2}} + 2 \sqrt{b}}{\sqrt{a}}$$
a^(3/2) + sqrt(b) + (b^(3/2) + 2*sqrt(b))/sqrt(a) + sqrt(b)/(a - b)
Potencias
[src]
3/2 ___ ___
3/2 ___ b \/ b 2*\/ b
a + \/ b + ----- + ----- + -------
___ a - b ___
\/ a \/ a
$$a^{\frac{3}{2}} + \sqrt{b} + \frac{\sqrt{b}}{a - b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}} + \frac{2 \sqrt{b}}{\sqrt{a}}$$
a^(3/2) + sqrt(b) + b^(3/2)/sqrt(a) + sqrt(b)/(a - b) + 2*sqrt(b)/sqrt(a)
Unión de expresiones racionales
[src]
___ ___ / 2 3/2\ ___ ___ ___
\/ a *\/ b + (a - b)*\a + b / + 2*\/ b *(a - b) + \/ a *\/ b *(a - b)
-------------------------------------------------------------------------
___
\/ a *(a - b)
$$\frac{\sqrt{a} \sqrt{b} \left(a - b\right) + \sqrt{a} \sqrt{b} + 2 \sqrt{b} \left(a - b\right) + \left(a - b\right) \left(a^{2} + b^{\frac{3}{2}}\right)}{\sqrt{a} \left(a - b\right)}$$
(sqrt(a)*sqrt(b) + (a - b)*(a^2 + b^(3/2)) + 2*sqrt(b)*(a - b) + sqrt(a)*sqrt(b)*(a - b))/(sqrt(a)*(a - b))
Denominador racional
[src]
___ / ___ ___ / 2 3/2\\ ___ ___ ___
\/ a *\\/ a *\/ b + (a - b)*\a + b // + a*\/ b *(a - b) + 2*\/ a *\/ b *(a - b)
-----------------------------------------------------------------------------------
a*(a - b)
$$\frac{2 \sqrt{a} \sqrt{b} \left(a - b\right) + \sqrt{a} \left(\sqrt{a} \sqrt{b} + \left(a - b\right) \left(a^{2} + b^{\frac{3}{2}}\right)\right) + a \sqrt{b} \left(a - b\right)}{a \left(a - b\right)}$$
(sqrt(a)*(sqrt(a)*sqrt(b) + (a - b)*(a^2 + b^(3/2))) + a*sqrt(b)*(a - b) + 2*sqrt(a)*sqrt(b)*(a - b))/(a*(a - b))
Parte trigonométrica
[src]
3/2 ___ ___
3/2 ___ b \/ b 2*\/ b
a + \/ b + ----- + ----- + -------
___ a - b ___
\/ a \/ a
$$a^{\frac{3}{2}} + \sqrt{b} + \frac{\sqrt{b}}{a - b} + \frac{b^{\frac{3}{2}}}{\sqrt{a}} + \frac{2 \sqrt{b}}{\sqrt{a}}$$
a^(3/2) + sqrt(b) + b^(3/2)/sqrt(a) + sqrt(b)/(a - b) + 2*sqrt(b)/sqrt(a)
Combinatoria
[src]
3 5/2 3/2 3/2 ___ ___ 3/2 ___ 2 ___ 3/2 ___
a - b - 2*b + a*b + \/ a *\/ b + a *\/ b - b*a - \/ a *b + 2*a*\/ b
--------------------------------------------------------------------------------------
___
\/ a *(a - b)
$$\frac{a^{\frac{3}{2}} \sqrt{b} - \sqrt{a} b^{\frac{3}{2}} + \sqrt{a} \sqrt{b} + a^{3} - a^{2} b + a b^{\frac{3}{2}} + 2 a \sqrt{b} - b^{\frac{5}{2}} - 2 b^{\frac{3}{2}}}{\sqrt{a} \left(a - b\right)}$$
(a^3 - b^(5/2) - 2*b^(3/2) + a*b^(3/2) + sqrt(a)*sqrt(b) + a^(3/2)*sqrt(b) - b*a^2 - sqrt(a)*b^(3/2) + 2*a*sqrt(b))/(sqrt(a)*(a - b))