Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
(sqrt((a*b*c+4)/a+4*(sqrt(b*c)/a)))/(sqrt(a*b*c)+2)
¿Cómo vas a descomponer esta (sqrt((a*b*c+4)/a+4*(sqrt(b*c)/a)))/(sqrt(a*b*c)+2) expresión en fracciones?
Solución
Ha introducido
[src]
_______________________
/ _____
/ a*b*c + 4 \/ b*c
/ --------- + 4*-------
\/ a a
----------------------------
_______
\/ a*b*c + 2
$$\frac{\sqrt{4 \frac{\sqrt{b c}}{a} + \frac{c a b + 4}{a}}}{\sqrt{c a b} + 2}$$
sqrt(((a*b)*c + 4)/a + 4*(sqrt(b*c)/a))/(sqrt((a*b)*c) + 2)
Simplificación general
[src]
_______________________
/ _____
/ 4 + 4*\/ b*c + a*b*c
/ ---------------------
\/ a
----------------------------
_______
2 + \/ a*b*c
$$\frac{\sqrt{\frac{a b c + 4 \sqrt{b c} + 4}{a}}}{\sqrt{a b c} + 2}$$
sqrt((4 + 4*sqrt(b*c) + a*b*c)/a)/(2 + sqrt(a*b*c))
Respuesta numérica
[src]
2.0*((b*c)^0.5/a + 0.25*(4.0 + a*b*c)/a)^0.5/(2.0 + (a*b*c)^0.5)
2.0*((b*c)^0.5/a + 0.25*(4.0 + a*b*c)/a)^0.5/(2.0 + (a*b*c)^0.5)
Parte trigonométrica
[src]
_______________________
/ _____
/ 4 + a*b*c 4*\/ b*c
/ --------- + ---------
\/ a a
----------------------------
_______
2 + \/ a*b*c
$$\frac{\sqrt{\frac{4 \sqrt{b c}}{a} + \frac{a b c + 4}{a}}}{\sqrt{a b c} + 2}$$
sqrt((4 + a*b*c)/a + 4*sqrt(b*c)/a)/(2 + sqrt(a*b*c))
Combinatoria
[src]
_____________________
/ _____
/ 4 4*\/ b*c
/ - + b*c + ---------
\/ a a
--------------------------
_______
2 + \/ a*b*c
$$\frac{\sqrt{b c + \frac{4 \sqrt{b c}}{a} + \frac{4}{a}}}{\sqrt{a b c} + 2}$$
sqrt(4/a + b*c + 4*sqrt(b*c)/a)/(2 + sqrt(a*b*c))
Compilar la expresión
[src]
_______________________
/ _____
/ 4 + 4*\/ b*c + a*b*c
/ ---------------------
\/ a
----------------------------
_______
2 + \/ a*b*c
$$\frac{\sqrt{\frac{a b c + 4 \sqrt{b c} + 4}{a}}}{\sqrt{a b c} + 2}$$
_______________________
/ _____
/ 4 + a*b*c 4*\/ b*c
/ --------- + ---------
\/ a a
----------------------------
_______
2 + \/ a*b*c
$$\frac{\sqrt{\frac{4 \sqrt{b c}}{a} + \frac{a b c + 4}{a}}}{\sqrt{a b c} + 2}$$
sqrt((4 + a*b*c)/a + 4*sqrt(b*c)/a)/(2 + sqrt(a*b*c))
Denominador común
[src]
_____________________
/ _____
/ 4 4*\/ b*c
/ - + b*c + ---------
\/ a a
--------------------------
_______
2 + \/ a*b*c
$$\frac{\sqrt{b c + \frac{4 \sqrt{b c}}{a} + \frac{4}{a}}}{\sqrt{a b c} + 2}$$
sqrt(4/a + b*c + 4*sqrt(b*c)/a)/(2 + sqrt(a*b*c))
Denominador racional
[src]
_____________________
/ _____
/ 4 4*\/ b*c / _______\
/ - + b*c + --------- *\-2 + \/ a*b*c /
\/ a a
-------------------------------------------
-4 + a*b*c
$$\frac{\left(\sqrt{a b c} - 2\right) \sqrt{b c + \frac{4 \sqrt{b c}}{a} + \frac{4}{a}}}{a b c - 4}$$
sqrt(4/a + b*c + 4*sqrt(b*c)/a)*(-2 + sqrt(a*b*c))/(-4 + a*b*c)
Potencias
[src]
_______________________
/ _____
/ 4 + a*b*c 4*\/ b*c
/ --------- + ---------
\/ a a
----------------------------
_______
2 + \/ a*b*c
$$\frac{\sqrt{\frac{4 \sqrt{b c}}{a} + \frac{a b c + 4}{a}}}{\sqrt{a b c} + 2}$$
sqrt((4 + a*b*c)/a + 4*sqrt(b*c)/a)/(2 + sqrt(a*b*c))
Unión de expresiones racionales
[src]
_______________________
/ _____
/ 4 + 4*\/ b*c + a*b*c
/ ---------------------
\/ a
----------------------------
_______
2 + \/ a*b*c
$$\frac{\sqrt{\frac{a b c + 4 \sqrt{b c} + 4}{a}}}{\sqrt{a b c} + 2}$$
sqrt((4 + 4*sqrt(b*c) + a*b*c)/a)/(2 + sqrt(a*b*c))