Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
(y/(4*y+16)+(y^2+16)/(4*y^2-64)-(4/(y^2-4*y)))/(3*y^2-24*y+48)/(y+4)
¿Cómo vas a descomponer esta (y/(4*y+16)+(y^2+16)/(4*y^2-64)-(4/(y^2-4*y)))/(3*y^2-24*y+48)/(y+4) expresión en fracciones?
Solución
Ha introducido
[src]
/ 2 \
| y y + 16 4 |
|-------- + --------- - --------|
|4*y + 16 2 2 |
| 4*y - 64 y - 4*y|
|-------------------------------|
| 2 |
\ 3*y - 24*y + 48 /
---------------------------------
y + 4
$$\frac{\frac{1}{\left(3 y^{2} - 24 y\right) + 48} \left(\left(\frac{y}{4 y + 16} + \frac{y^{2} + 16}{4 y^{2} - 64}\right) - \frac{4}{y^{2} - 4 y}\right)}{y + 4}$$
((y/(4*y + 16) + (y^2 + 16)/(4*y^2 - 64) - 4/(y^2 - 4*y))/(3*y^2 - 24*y + 48))/(y + 4)
Descomposición de una fracción
[src]
-1/(96*(4 + y)^2) - 1/(256*(-4 + y)) - 1/(768*(4 + y)) + 1/(48*(-4 + y)^2) + 1/(192*y)
$$- \frac{1}{768 \left(y + 4\right)} - \frac{1}{96 \left(y + 4\right)^{2}} - \frac{1}{256 \left(y - 4\right)} + \frac{1}{48 \left(y - 4\right)^{2}} + \frac{1}{192 y}$$
1 1 1 1 1
- ----------- - ------------ - ----------- + ------------ + -----
2 256*(-4 + y) 768*(4 + y) 2 192*y
96*(4 + y) 48*(-4 + y)
Simplificación general
[src]
2
8 + y + 2*y
----------------------
/ 4 2\
6*y*\256 + y - 32*y /
$$\frac{y^{2} + 2 y + 8}{6 y \left(y^{4} - 32 y^{2} + 256\right)}$$
(8 + y^2 + 2*y)/(6*y*(256 + y^4 - 32*y^2))
Parte trigonométrica
[src]
2
4 y 16 + y
- -------- + -------- + ----------
2 16 + 4*y 2
y - 4*y -64 + 4*y
----------------------------------
/ 2\
(4 + y)*\48 - 24*y + 3*y /
$$\frac{\frac{y}{4 y + 16} + \frac{y^{2} + 16}{4 y^{2} - 64} - \frac{4}{y^{2} - 4 y}}{\left(y + 4\right) \left(3 y^{2} - 24 y + 48\right)}$$
(-4/(y^2 - 4*y) + y/(16 + 4*y) + (16 + y^2)/(-64 + 4*y^2))/((4 + y)*(48 - 24*y + 3*y^2))
Denominador racional
[src]
/ 2 \ / / 2\ / 2\ \ / 2\
\y - 4*y/*\y*\-64 + 4*y / + \16 + y /*(16 + 4*y)/ - 4*\-64 + 4*y /*(16 + 4*y)
------------------------------------------------------------------------------
/ 2\ / 2 \ / 2\
\-64 + 4*y /*(4 + y)*(16 + 4*y)*\y - 4*y/*\48 - 24*y + 3*y /
$$\frac{- 4 \left(4 y + 16\right) \left(4 y^{2} - 64\right) + \left(y^{2} - 4 y\right) \left(y \left(4 y^{2} - 64\right) + \left(4 y + 16\right) \left(y^{2} + 16\right)\right)}{\left(y + 4\right) \left(4 y + 16\right) \left(y^{2} - 4 y\right) \left(4 y^{2} - 64\right) \left(3 y^{2} - 24 y + 48\right)}$$
((y^2 - 4*y)*(y*(-64 + 4*y^2) + (16 + y^2)*(16 + 4*y)) - 4*(-64 + 4*y^2)*(16 + 4*y))/((-64 + 4*y^2)*(4 + y)*(16 + 4*y)*(y^2 - 4*y)*(48 - 24*y + 3*y^2))
Combinatoria
[src]
2
8 + y + 2*y
----------------------
2 2
6*y*(-4 + y) *(4 + y)
$$\frac{y^{2} + 2 y + 8}{6 y \left(y - 4\right)^{2} \left(y + 4\right)^{2}}$$
(8 + y^2 + 2*y)/(6*y*(-4 + y)^2*(4 + y)^2)
Potencias
[src]
2
4 y 16 + y
- -------- + -------- + ----------
2 16 + 4*y 2
y - 4*y -64 + 4*y
----------------------------------
/ 2\
(4 + y)*\48 - 24*y + 3*y /
$$\frac{\frac{y}{4 y + 16} + \frac{y^{2} + 16}{4 y^{2} - 64} - \frac{4}{y^{2} - 4 y}}{\left(y + 4\right) \left(3 y^{2} - 24 y + 48\right)}$$
(-4/(y^2 - 4*y) + y/(16 + 4*y) + (16 + y^2)/(-64 + 4*y^2))/((4 + y)*(48 - 24*y + 3*y^2))
Unión de expresiones racionales
[src]
/ 2\ / / 2\ / 2\\
- 16*\-16 + y /*(4 + y) + y*(-4 + y)*\y*\-16 + y / + (4 + y)*\16 + y //
-----------------------------------------------------------------------
/ 2\ 2
12*y*\-16 + y /*(-4 + y)*(4 + y) *(16 + y*(-8 + y))
$$\frac{y \left(y - 4\right) \left(y \left(y^{2} - 16\right) + \left(y + 4\right) \left(y^{2} + 16\right)\right) - 16 \left(y + 4\right) \left(y^{2} - 16\right)}{12 y \left(y - 4\right) \left(y + 4\right)^{2} \left(y^{2} - 16\right) \left(y \left(y - 8\right) + 16\right)}$$
(-16*(-16 + y^2)*(4 + y) + y*(-4 + y)*(y*(-16 + y^2) + (4 + y)*(16 + y^2)))/(12*y*(-16 + y^2)*(-4 + y)*(4 + y)^2*(16 + y*(-8 + y)))
Denominador común
[src]
2
8 + y + 2*y
------------------------
3 5
- 192*y + 6*y + 1536*y
$$\frac{y^{2} + 2 y + 8}{6 y^{5} - 192 y^{3} + 1536 y}$$
(8 + y^2 + 2*y)/(-192*y^3 + 6*y^5 + 1536*y)
Compilar la expresión
[src]
2
4 y 16 + y
- -------- + -------- + ----------
2 16 + 4*y 2
y - 4*y -64 + 4*y
----------------------------------
/ 2\
(4 + y)*\48 - 24*y + 3*y /
$$\frac{\frac{y}{4 y + 16} + \frac{y^{2} + 16}{4 y^{2} - 64} - \frac{4}{y^{2} - 4 y}}{\left(y + 4\right) \left(3 y^{2} - 24 y + 48\right)}$$
(-4/(y^2 - 4*y) + y/(16 + 4*y) + (16 + y^2)/(-64 + 4*y^2))/((4 + y)*(48 - 24*y + 3*y^2))
Respuesta numérica
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(-4.0/(y^2 - 4.0*y) + y/(16.0 + 4.0*y) + (16.0 + y^2)/(-64.0 + 4.0*y^2))/((4.0 + y)*(48.0 + 3.0*y^2 - 24.0*y))
(-4.0/(y^2 - 4.0*y) + y/(16.0 + 4.0*y) + (16.0 + y^2)/(-64.0 + 4.0*y^2))/((4.0 + y)*(48.0 + 3.0*y^2 - 24.0*y))