Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(x*sqrt(a)/(5*x-3)^4)*(5*x-3)^4*(sqrt(a)/(2*(5*x-3)^4)-10*x*sqrt(a)/(5*x-3)^5)/(sqrt(a)*x)
¿Cómo vas a descomponer esta sqrt(x*sqrt(a)/(5*x-3)^4)*(5*x-3)^4*(sqrt(a)/(2*(5*x-3)^4)-10*x*sqrt(a)/(5*x-3)^5)/(sqrt(a)*x) expresión en fracciones?
Solución
Ha introducido
[src]
____________
/ ___ / ___ ___\
/ x*\/ a 4 | \/ a 10*x*\/ a |
/ ---------- *(5*x - 3) *|------------ - ----------|
/ 4 | 4 5|
\/ (5*x - 3) \2*(5*x - 3) (5*x - 3) /
---------------------------------------------------------
___
\/ a *x
$$\frac{\sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{4} \left(\frac{\sqrt{a}}{2 \left(5 x - 3\right)^{4}} - \frac{\sqrt{a} 10 x}{\left(5 x - 3\right)^{5}}\right)}{\sqrt{a} x}$$
((sqrt((x*sqrt(a))/(5*x - 3)^4)*(5*x - 3)^4)*(sqrt(a)/((2*(5*x - 3)^4)) - (10*x)*sqrt(a)/(5*x - 3)^5))/((sqrt(a)*x))
Simplificación general
[src]
_____________
/ ___
/ x*\/ a
-3* / ----------- *(1 + 5*x)
/ 4
\/ (-3 + 5*x)
--------------------------------
2*x*(-3 + 5*x)
$$- \frac{3 \sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x + 1\right)}{2 x \left(5 x - 3\right)}$$
-3*sqrt(x*sqrt(a)/(-3 + 5*x)^4)*(1 + 5*x)/(2*x*(-3 + 5*x))
Respuesta numérica
[src]
25.0*a^(-0.5)*(x*a^0.5/(-0.6 + x)^4)^0.5*(-0.6 + x)^4*(0.0008*a^0.5/(-0.6 + x)^4 - 0.0032*x*a^0.5/(-0.6 + x)^5)/x
25.0*a^(-0.5)*(x*a^0.5/(-0.6 + x)^4)^0.5*(-0.6 + x)^4*(0.0008*a^0.5/(-0.6 + x)^4 - 0.0032*x*a^0.5/(-0.6 + x)^5)/x
Denominador común
[src]
/ _________________________________________ _________________________________________\
| / ___ / ___ |
| / x*\/ a / x*\/ a |
-|3* / --------------------------------------- + 15*x* / --------------------------------------- |
| / 3 4 2 / 3 4 2 |
\ \/ 81 - 1500*x - 540*x + 625*x + 1350*x \/ 81 - 1500*x - 540*x + 625*x + 1350*x /
------------------------------------------------------------------------------------------------------------
2
-6*x + 10*x
$$- \frac{15 x \sqrt{\frac{\sqrt{a} x}{625 x^{4} - 1500 x^{3} + 1350 x^{2} - 540 x + 81}} + 3 \sqrt{\frac{\sqrt{a} x}{625 x^{4} - 1500 x^{3} + 1350 x^{2} - 540 x + 81}}}{10 x^{2} - 6 x}$$
-(3*sqrt(x*sqrt(a)/(81 - 1500*x^3 - 540*x + 625*x^4 + 1350*x^2)) + 15*x*sqrt(x*sqrt(a)/(81 - 1500*x^3 - 540*x + 625*x^4 + 1350*x^2)))/(-6*x + 10*x^2)
Unión de expresiones racionales
[src]
_____________
/ ___
/ x*\/ a
3* / ----------- *(-1 - 5*x)
/ 4
\/ (-3 + 5*x)
--------------------------------
2*x*(-3 + 5*x)
$$\frac{3 \sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(- 5 x - 1\right)}{2 x \left(5 x - 3\right)}$$
3*sqrt(x*sqrt(a)/(-3 + 5*x)^4)*(-1 - 5*x)/(2*x*(-3 + 5*x))
Parte trigonométrica
[src]
_____________
/ ___ / ___ ___\
/ x*\/ a 4 | \/ a 10*x*\/ a |
/ ----------- *(-3 + 5*x) *|------------- - -----------|
/ 4 | 4 5|
\/ (-3 + 5*x) \2*(-3 + 5*x) (-3 + 5*x) /
-------------------------------------------------------------
___
\/ a *x
$$\frac{\sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{4} \left(- \frac{10 \sqrt{a} x}{\left(5 x - 3\right)^{5}} + \frac{\sqrt{a}}{2 \left(5 x - 3\right)^{4}}\right)}{\sqrt{a} x}$$
sqrt(x*sqrt(a)/(-3 + 5*x)^4)*(-3 + 5*x)^4*(sqrt(a)/(2*(-3 + 5*x)^4) - 10*x*sqrt(a)/(-3 + 5*x)^5)/(sqrt(a)*x)
Potencias
[src]
_____________
/ ___ / ___ ___\
/ x*\/ a 4 | \/ a 10*x*\/ a |
/ ----------- *(-3 + 5*x) *|------------- - -----------|
/ 4 | 4 5|
\/ (-3 + 5*x) \2*(-3 + 5*x) (-3 + 5*x) /
-------------------------------------------------------------
___
\/ a *x
$$\frac{\sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{4} \left(- \frac{10 \sqrt{a} x}{\left(5 x - 3\right)^{5}} + \frac{\sqrt{a}}{2 \left(5 x - 3\right)^{4}}\right)}{\sqrt{a} x}$$
sqrt(x*sqrt(a)/(-3 + 5*x)^4)*(-3 + 5*x)^4*(sqrt(a)/(2*(-3 + 5*x)^4) - 10*x*sqrt(a)/(-3 + 5*x)^5)/(sqrt(a)*x)
Combinatoria
[src]
_________________________________________
/ ___
/ x*\/ a
-3* / --------------------------------------- *(1 + 5*x)
/ 3 4 2
\/ 81 - 1500*x - 540*x + 625*x + 1350*x
------------------------------------------------------------
2*x*(-3 + 5*x)
$$- \frac{3 \sqrt{\frac{\sqrt{a} x}{625 x^{4} - 1500 x^{3} + 1350 x^{2} - 540 x + 81}} \left(5 x + 1\right)}{2 x \left(5 x - 3\right)}$$
-3*sqrt(x*sqrt(a)/(81 - 1500*x^3 - 540*x + 625*x^4 + 1350*x^2))*(1 + 5*x)/(2*x*(-3 + 5*x))
Denominador racional
[src]
____________ ____________
/ ___ / ___
___ / x*\/ a 5 ___ / x*\/ a 4
\/ a * / ---------- *(-3 + 5*x) - 20*x*\/ a * / ---------- *(-3 + 5*x)
/ 4 / 4
\/ (5*x - 3) \/ (5*x - 3)
--------------------------------------------------------------------------------
___ 5
2*\/ a *x*(-3 + 5*x)
$$\frac{- 20 \sqrt{a} x \sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{4} + \sqrt{a} \sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{5}}{2 \sqrt{a} x \left(5 x - 3\right)^{5}}$$
(sqrt(a)*sqrt(x*sqrt(a)/(5*x - 3)^4)*(-3 + 5*x)^5 - 20*x*sqrt(a)*sqrt(x*sqrt(a)/(5*x - 3)^4)*(-3 + 5*x)^4)/(2*sqrt(a)*x*(-3 + 5*x)^5)
Compilar la expresión
[src]
_____________
/ ___ / ___ ___\
/ x*\/ a 4 | \/ a 10*x*\/ a |
/ ----------- *(-3 + 5*x) *|------------- - -----------|
/ 4 | 4 5|
\/ (-3 + 5*x) \2*(-3 + 5*x) (-3 + 5*x) /
-------------------------------------------------------------
___
\/ a *x
$$\frac{\sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{4} \left(- \frac{10 \sqrt{a} x}{\left(5 x - 3\right)^{5}} + \frac{\sqrt{a}}{2 \left(5 x - 3\right)^{4}}\right)}{\sqrt{a} x}$$
_____________
/ ___
/ x*\/ a 4 / 1 10*x \
/ ----------- *(-3 + 5*x) *|------------- - -----------|
/ 4 | 4 5|
\/ (-3 + 5*x) \2*(-3 + 5*x) (-3 + 5*x) /
-------------------------------------------------------------
x
$$\frac{\sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{4} \left(- \frac{10 x}{\left(5 x - 3\right)^{5}} + \frac{1}{2 \left(5 x - 3\right)^{4}}\right)}{x}$$
sqrt(x*sqrt(a)/(-3 + 5*x)^4)*(-3 + 5*x)^4*(1/(2*(-3 + 5*x)^4) - 10*x/(-3 + 5*x)^5)/x