Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(a*a-(x-a)/2*(x-a)/2)/2+(a+x)*(-x/4+a/4)/(2*sqrt(a*a-(x-a)/2*(x-a)/2))
¿Cómo vas a descomponer esta sqrt(a*a-(x-a)/2*(x-a)/2)/2+(a+x)*(-x/4+a/4)/(2*sqrt(a*a-(x-a)/2*(x-a)/2)) expresión en fracciones?
Solución
Ha introducido
[src]
_____________________
/ x - a
/ -----*(x - a)
/ 2 /-x a\
/ a*a - ------------- (a + x)*|--- + -|
\/ 2 \ 4 4/
--------------------------- + -----------------------------
2 _____________________
/ x - a
/ -----*(x - a)
/ 2
2* / a*a - -------------
\/ 2
$$\frac{\left(a + x\right) \left(\frac{a}{4} + \frac{\left(-1\right) x}{4}\right)}{2 \sqrt{a a - \frac{\frac{- a + x}{2} \left(- a + x\right)}{2}}} + \frac{\sqrt{a a - \frac{\frac{- a + x}{2} \left(- a + x\right)}{2}}}{2}$$
sqrt(a*a - ((x - a)/2)*(x - a)/2)/2 + ((a + x)*((-x)/4 + a/4))/((2*sqrt(a*a - ((x - a)/2)*(x - a)/2)))
Simplificación general
[src]
2 2
- (a - x) + 4*a + (a + x)*(a - x)
-----------------------------------
___________________
/ 2 2
4*\/ - (a - x) + 4*a
$$\frac{4 a^{2} - \left(a - x\right)^{2} + \left(a - x\right) \left(a + x\right)}{4 \sqrt{4 a^{2} - \left(a - x\right)^{2}}}$$
(-(a - x)^2 + 4*a^2 + (a + x)*(a - x))/(4*sqrt(-(a - x)^2 + 4*a^2))
Denominador común
[src]
/ 2 2 \
-\x - 2*a - a*x/
--------------------------
_____________________
/ 2 2
2*\/ - x + 3*a + 2*a*x
$$- \frac{- 2 a^{2} - a x + x^{2}}{2 \sqrt{3 a^{2} + 2 a x - x^{2}}}$$
-(x^2 - 2*a^2 - a*x)/(2*sqrt(-x^2 + 3*a^2 + 2*a*x))
Parte trigonométrica
[src]
______________________
/ /x a\
/ (x - a)*|- - -|
/ 2 \2 2/ / x a\
/ a - --------------- (a + x)*|- - + -|
\/ 2 \ 4 4/
---------------------------- + ------------------------------
2 ______________________
/ /x a\
/ (x - a)*|- - -|
/ 2 \2 2/
2* / a - ---------------
\/ 2
$$\frac{\left(\frac{a}{4} - \frac{x}{4}\right) \left(a + x\right)}{2 \sqrt{a^{2} - \frac{\left(- a + x\right) \left(- \frac{a}{2} + \frac{x}{2}\right)}{2}}} + \frac{\sqrt{a^{2} - \frac{\left(- a + x\right) \left(- \frac{a}{2} + \frac{x}{2}\right)}{2}}}{2}$$
sqrt(a^2 - (x - a)*(x/2 - a/2)/2)/2 + (a + x)*(-x/4 + a/4)/(2*sqrt(a^2 - (x - a)*(x/2 - a/2)/2))
Denominador racional
[src]
_____________________ _____________________ _____________________
2 / 2 2 2 / 2 2 2 / 2 2
- 8*x *\/ - x + 3*a + 2*a*x - 8*(a - x) *\/ - x + 3*a + 2*a*x + 40*a *\/ - x + 3*a + 2*a*x
------------------------------------------------------------------------------------------------------
2 2
- 32*x + 96*a + 64*a*x
$$\frac{40 a^{2} \sqrt{3 a^{2} + 2 a x - x^{2}} - 8 x^{2} \sqrt{3 a^{2} + 2 a x - x^{2}} - 8 \left(a - x\right)^{2} \sqrt{3 a^{2} + 2 a x - x^{2}}}{96 a^{2} + 64 a x - 32 x^{2}}$$
(-8*x^2*sqrt(-x^2 + 3*a^2 + 2*a*x) - 8*(a - x)^2*sqrt(-x^2 + 3*a^2 + 2*a*x) + 40*a^2*sqrt(-x^2 + 3*a^2 + 2*a*x))/(-32*x^2 + 96*a^2 + 64*a*x)
Compilar la expresión
[src]
______________________
/ /x a\
/ (x - a)*|- - -|
/ 2 \2 2/ / x a\
/ a - --------------- (a + x)*|- - + -|
\/ 2 \ 4 4/
---------------------------- + ------------------------------
2 ______________________
/ /x a\
/ (x - a)*|- - -|
/ 2 \2 2/
2* / a - ---------------
\/ 2
$$\frac{\left(\frac{a}{4} - \frac{x}{4}\right) \left(a + x\right)}{2 \sqrt{a^{2} - \frac{\left(- a + x\right) \left(- \frac{a}{2} + \frac{x}{2}\right)}{2}}} + \frac{\sqrt{a^{2} - \frac{\left(- a + x\right) \left(- \frac{a}{2} + \frac{x}{2}\right)}{2}}}{2}$$
sqrt(a^2 - (x - a)*(x/2 - a/2)/2)/2 + (a + x)*(-x/4 + a/4)/(2*sqrt(a^2 - (x - a)*(x/2 - a/2)/2))
Unión de expresiones racionales
[src]
2 2
- (x - a) + 4*a + (a + x)*(a - x)
-----------------------------------
___________________
/ 2 2
4*\/ - (x - a) + 4*a
$$\frac{4 a^{2} - \left(- a + x\right)^{2} + \left(a - x\right) \left(a + x\right)}{4 \sqrt{4 a^{2} - \left(- a + x\right)^{2}}}$$
(-(x - a)^2 + 4*a^2 + (a + x)*(a - x))/(4*sqrt(-(x - a)^2 + 4*a^2))
Combinatoria
[src]
-(a + x)*(x - 2*a)
------------------------
____________________
2*\/ -(a + x)*(x - 3*a)
$$- \frac{\left(- 2 a + x\right) \left(a + x\right)}{2 \sqrt{- \left(- 3 a + x\right) \left(a + x\right)}}$$
-(a + x)*(x - 2*a)/(2*sqrt(-(a + x)*(x - 3*a)))
Respuesta numérica
[src]
0.5*(a^2 - 0.25*(x - a)^2)^0.5 + 0.5*(a^2 - 0.25*(x - a)^2)^(-0.5)*(a + x)*(0.25*a - 0.25*x)
0.5*(a^2 - 0.25*(x - a)^2)^0.5 + 0.5*(a^2 - 0.25*(x - a)^2)^(-0.5)*(a + x)*(0.25*a - 0.25*x)
Potencias
[src]
______________________
/ /x a\
/ (x - a)*|- - -|
/ 2 \2 2/ / x a\
/ a - --------------- (a + x)*|- - + -|
\/ 2 \ 4 4/
---------------------------- + ------------------------------
2 ______________________
/ /x a\
/ (x - a)*|- - -|
/ 2 \2 2/
2* / a - ---------------
\/ 2
$$\frac{\left(\frac{a}{4} - \frac{x}{4}\right) \left(a + x\right)}{2 \sqrt{a^{2} - \frac{\left(- a + x\right) \left(- \frac{a}{2} + \frac{x}{2}\right)}{2}}} + \frac{\sqrt{a^{2} - \frac{\left(- a + x\right) \left(- \frac{a}{2} + \frac{x}{2}\right)}{2}}}{2}$$
sqrt(a^2 - (x - a)*(x/2 - a/2)/2)/2 + (a + x)*(-x/4 + a/4)/(2*sqrt(a^2 - (x - a)*(x/2 - a/2)/2))