Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)
¿Cómo vas a descomponer esta (z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z) expresión en fracciones?
Solución
Ha introducido
[src]
2
z - 4*z + 16 / 2 \
-------------*\4*z + z/
2
16*z - 1 z + 4
------------------------ - --------
3 2
z + 64 4*z - z
$$\frac{\frac{\left(z^{2} - 4 z\right) + 16}{16 z^{2} - 1} \left(4 z^{2} + z\right)}{z^{3} + 64} - \frac{z + 4}{4 z^{2} - z}$$
(((z^2 - 4*z + 16)/(16*z^2 - 1))*(4*z^2 + z))/(z^3 + 64) - (z + 4)/(4*z^2 - z)
Simplificación general
[src]
-(16 + 8*z) -------------------- / 2 \ z*\-4 + 4*z + 15*z/
$$- \frac{8 z + 16}{z \left(4 z^{2} + 15 z - 4\right)}$$
-(16 + 8*z)/(z*(-4 + 4*z^2 + 15*z))
Descomposición de una fracción
[src]
4/z - 288/(17*(-1 + 4*z)) + 4/(17*(4 + z))
$$- \frac{288}{17 \left(4 z - 1\right)} + \frac{4}{17 \left(z + 4\right)} + \frac{4}{z}$$
4 288 4 - - ------------- + ---------- z 17*(-1 + 4*z) 17*(4 + z)
Respuesta numérica
[src]
-(4.0 + z)/(-z + 4.0*z^2) + (z + 4.0*z^2)*(16.0 + z^2 - 4.0*z)/((64.0 + z^3)*(-1.0 + 16.0*z^2))
-(4.0 + z)/(-z + 4.0*z^2) + (z + 4.0*z^2)*(16.0 + z^2 - 4.0*z)/((64.0 + z^3)*(-1.0 + 16.0*z^2))
Potencias
[src]
/ 2\ / 2 \
4 + z \z + 4*z /*\16 + z - 4*z/
- --------- + --------------------------
2 / 2\ / 3\
-z + 4*z \-1 + 16*z /*\64 + z /
$$- \frac{z + 4}{4 z^{2} - z} + \frac{\left(4 z^{2} + z\right) \left(z^{2} - 4 z + 16\right)}{\left(16 z^{2} - 1\right) \left(z^{3} + 64\right)}$$
/ 2\ / 2 \
-4 - z \z + 4*z /*\16 + z - 4*z/
--------- + --------------------------
2 / 2\ / 3\
-z + 4*z \-1 + 16*z /*\64 + z /
$$\frac{- z - 4}{4 z^{2} - z} + \frac{\left(4 z^{2} + z\right) \left(z^{2} - 4 z + 16\right)}{\left(16 z^{2} - 1\right) \left(z^{3} + 64\right)}$$
(-4 - z)/(-z + 4*z^2) + (z + 4*z^2)*(16 + z^2 - 4*z)/((-1 + 16*z^2)*(64 + z^3))
Denominador común
[src]
-(16 + 8*z)
-------------------
3 2
-4*z + 4*z + 15*z
$$- \frac{8 z + 16}{4 z^{3} + 15 z^{2} - 4 z}$$
-(16 + 8*z)/(-4*z + 4*z^3 + 15*z^2)
Denominador racional
[src]
/ 2\ / 3\ / 2\ / 2\ / 2 \
\-1 + 16*z /*(-4 - z)*\64 + z / + \z + 4*z /*\-z + 4*z /*\16 + z - 4*z/
------------------------------------------------------------------------
/ 2\ / 3\ / 2\
\-1 + 16*z /*\64 + z /*\-z + 4*z /
$$\frac{\left(- z - 4\right) \left(16 z^{2} - 1\right) \left(z^{3} + 64\right) + \left(4 z^{2} - z\right) \left(4 z^{2} + z\right) \left(z^{2} - 4 z + 16\right)}{\left(4 z^{2} - z\right) \left(16 z^{2} - 1\right) \left(z^{3} + 64\right)}$$
((-1 + 16*z^2)*(-4 - z)*(64 + z^3) + (z + 4*z^2)*(-z + 4*z^2)*(16 + z^2 - 4*z))/((-1 + 16*z^2)*(64 + z^3)*(-z + 4*z^2))
Compilar la expresión
[src]
/ 2\ / 2 \
4 + z \z + 4*z /*\16 + z - 4*z/
- --------- + --------------------------
2 / 2\ / 3\
-z + 4*z \-1 + 16*z /*\64 + z /
$$- \frac{z + 4}{4 z^{2} - z} + \frac{\left(4 z^{2} + z\right) \left(z^{2} - 4 z + 16\right)}{\left(16 z^{2} - 1\right) \left(z^{3} + 64\right)}$$
-(4 + z)/(-z + 4*z^2) + (z + 4*z^2)*(16 + z^2 - 4*z)/((-1 + 16*z^2)*(64 + z^3))
Unión de expresiones racionales
[src]
/ 2\ / 3\ 2
- \-1 + 16*z /*(4 + z)*\64 + z / + z *(1 + 4*z)*(-1 + 4*z)*(16 + z*(-4 + z))
----------------------------------------------------------------------------
/ 2\ / 3\
z*(-1 + 4*z)*\-1 + 16*z /*\64 + z /
$$\frac{z^{2} \left(4 z - 1\right) \left(4 z + 1\right) \left(z \left(z - 4\right) + 16\right) - \left(z + 4\right) \left(16 z^{2} - 1\right) \left(z^{3} + 64\right)}{z \left(4 z - 1\right) \left(16 z^{2} - 1\right) \left(z^{3} + 64\right)}$$
(-(-1 + 16*z^2)*(4 + z)*(64 + z^3) + z^2*(1 + 4*z)*(-1 + 4*z)*(16 + z*(-4 + z)))/(z*(-1 + 4*z)*(-1 + 16*z^2)*(64 + z^3))
Parte trigonométrica
[src]
/ 2\ / 2 \
4 + z \z + 4*z /*\16 + z - 4*z/
- --------- + --------------------------
2 / 2\ / 3\
-z + 4*z \-1 + 16*z /*\64 + z /
$$- \frac{z + 4}{4 z^{2} - z} + \frac{\left(4 z^{2} + z\right) \left(z^{2} - 4 z + 16\right)}{\left(16 z^{2} - 1\right) \left(z^{3} + 64\right)}$$
-(4 + z)/(-z + 4*z^2) + (z + 4*z^2)*(16 + z^2 - 4*z)/((-1 + 16*z^2)*(64 + z^3))
Combinatoria
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-8*(2 + z) -------------------- z*(-1 + 4*z)*(4 + z)
$$- \frac{8 \left(z + 2\right)}{z \left(z + 4\right) \left(4 z - 1\right)}$$
-8*(2 + z)/(z*(-1 + 4*z)*(4 + z))