Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)
¿Cómo vas a descomponer esta z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z) expresión en fracciones?
Solución
Ha introducido
[src]
2
z 16
z - -- + 16*z + ----------------------------------
2 z 2 2 2
-*z - 4 - z + 2*z - 8 - -- + 2*z
2 2
z
$$\left(16 z + \left(- \frac{z^{2}}{2} + z\right)\right) + \frac{16}{2 z + \left(\left(\left(2 z^{2} + \left(- z^{2} + \left(z \frac{z}{2} - 4\right)\right)\right) - 8\right) - \frac{2}{z^{2}}\right)}$$
z - z^2/2 + 16*z + 16/((z/2)*z - 4 - z^2 + 2*z^2 - 8 - 2/z^2 + 2*z)
Descomposición de una fracción
[src]
17*z - z^2/2 + 32*z^2/(-4 - 24*z^2 + 3*z^4 + 4*z^3)
$$- \frac{z^{2}}{2} + \frac{32 z^{2}}{3 z^{4} + 4 z^{3} - 24 z^{2} - 4} + 17 z$$
2 2
z 32*z
17*z - -- + ------------------------
2 2 4 3
-4 - 24*z + 3*z + 4*z
Simplificación general
[src]
/ / 2 / 2 \\ \
z*\64*z + \-4 + z *\-24 + 3*z + 4*z//*(34 - z)/
------------------------------------------------
/ 2 / 2 \\
2*\-4 + z *\-24 + 3*z + 4*z//
$$\frac{z \left(64 z + \left(34 - z\right) \left(z^{2} \left(3 z^{2} + 4 z - 24\right) - 4\right)\right)}{2 \left(z^{2} \left(3 z^{2} + 4 z - 24\right) - 4\right)}$$
z*(64*z + (-4 + z^2*(-24 + 3*z^2 + 4*z))*(34 - z))/(2*(-4 + z^2*(-24 + 3*z^2 + 4*z)))
Respuesta numérica
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16.0/(-12.0 + 2.0*z + 1.5*z^2 - 2.0/z^2) + 17.0*z - 0.5*z^2
16.0/(-12.0 + 2.0*z + 1.5*z^2 - 2.0/z^2) + 17.0*z - 0.5*z^2
Parte trigonométrica
[src]
2
16 z
--------------------- + 17*z - --
2 2
2 3*z
-12 - -- + 2*z + ----
2 2
z
$$- \frac{z^{2}}{2} + 17 z + \frac{16}{\frac{3 z^{2}}{2} + 2 z - 12 - \frac{2}{z^{2}}}$$
16/(-12 - 2/z^2 + 2*z + 3*z^2/2) + 17*z - z^2/2
Denominador común
[src]
2 2
z 32*z
17*z - -- + ------------------------
2 2 4 3
-4 - 24*z + 3*z + 4*z
$$- \frac{z^{2}}{2} + \frac{32 z^{2}}{3 z^{4} + 4 z^{3} - 24 z^{2} - 4} + 17 z$$
17*z - z^2/2 + 32*z^2/(-4 - 24*z^2 + 3*z^4 + 4*z^3)
Compilar la expresión
[src]
2
16 z
--------------------- + 17*z - --
2 2
2 3*z
-12 - -- + 2*z + ----
2 2
z
$$- \frac{z^{2}}{2} + 17 z + \frac{16}{\frac{3 z^{2}}{2} + 2 z - 12 - \frac{2}{z^{2}}}$$
16/(-12 - 2/z^2 + 2*z + 3*z^2/2) + 17*z - z^2/2
Denominador racional
[src]
/ 3 4 5 2\
-z*\136 - 160*z - 98*z - 68*z + 3*z + 816*z /
-------------------------------------------------
2 4 3
-8 - 48*z + 6*z + 8*z
$$- \frac{z \left(3 z^{5} - 98 z^{4} - 160 z^{3} + 816 z^{2} - 68 z + 136\right)}{6 z^{4} + 8 z^{3} - 48 z^{2} - 8}$$
-z*(136 - 160*z^3 - 98*z^4 - 68*z + 3*z^5 + 816*z^2)/(-8 - 48*z^2 + 6*z^4 + 8*z^3)
Potencias
[src]
2
16 z
--------------------- + 17*z - --
2 2
2 3*z
-12 - -- + 2*z + ----
2 2
z
$$- \frac{z^{2}}{2} + 17 z + \frac{16}{\frac{3 z^{2}}{2} + 2 z - 12 - \frac{2}{z^{2}}}$$
16/(-12 - 2/z^2 + 2*z + 3*z^2/2) + 17*z - z^2/2
Unión de expresiones racionales
[src]
/ / 3 2 / 2\\\
z*\64*z + (34 - z)*\-4 + 4*z + 3*z *\-8 + z ///
------------------------------------------------
/ 3 2 / 2\\
2*\-4 + 4*z + 3*z *\-8 + z //
$$\frac{z \left(64 z + \left(34 - z\right) \left(4 z^{3} + 3 z^{2} \left(z^{2} - 8\right) - 4\right)\right)}{2 \left(4 z^{3} + 3 z^{2} \left(z^{2} - 8\right) - 4\right)}$$
z*(64*z + (34 - z)*(-4 + 4*z^3 + 3*z^2*(-8 + z^2)))/(2*(-4 + 4*z^3 + 3*z^2*(-8 + z^2)))
Combinatoria
[src]
/ 3 4 5 2\
-z*\136 - 160*z - 98*z - 68*z + 3*z + 816*z /
-------------------------------------------------
/ 2 4 3\
2*\-4 - 24*z + 3*z + 4*z /
$$- \frac{z \left(3 z^{5} - 98 z^{4} - 160 z^{3} + 816 z^{2} - 68 z + 136\right)}{2 \left(3 z^{4} + 4 z^{3} - 24 z^{2} - 4\right)}$$
-z*(136 - 160*z^3 - 98*z^4 - 68*z + 3*z^5 + 816*z^2)/(2*(-4 - 24*z^2 + 3*z^4 + 4*z^3))