Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(z+1)/2-log(z)+log(z-1)/2+1/(2*z^2)
¿Cómo vas a descomponer esta log(z+1)/2-log(z)+log(z-1)/2+1/(2*z^2) expresión en fracciones?
Solución
Ha introducido
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log(z + 1) log(z - 1) 1
---------- - log(z) + ---------- + ----
2 2 2
2*z
$$\left(\left(- \log{\left(z \right)} + \frac{\log{\left(z + 1 \right)}}{2}\right) + \frac{\log{\left(z - 1 \right)}}{2}\right) + \frac{1}{2 z^{2}}$$
log(z + 1)/2 - log(z) + log(z - 1)/2 + 1/(2*z^2)
Simplificación general
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1 log(1 + z) log(-1 + z) ---- + ---------- + ----------- - log(z) 2 2 2 2*z
$$- \log{\left(z \right)} + \frac{\log{\left(z - 1 \right)}}{2} + \frac{\log{\left(z + 1 \right)}}{2} + \frac{1}{2 z^{2}}$$
1/(2*z^2) + log(1 + z)/2 + log(-1 + z)/2 - log(z)
Respuesta numérica
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-log(z) + 0.5/z^2 + 0.5*log(z + 1) + 0.5*log(z - 1)
-log(z) + 0.5/z^2 + 0.5*log(z + 1) + 0.5*log(z - 1)
Parte trigonométrica
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1 log(1 + z) log(-1 + z) ---- + ---------- + ----------- - log(z) 2 2 2 2*z
$$- \log{\left(z \right)} + \frac{\log{\left(z - 1 \right)}}{2} + \frac{\log{\left(z + 1 \right)}}{2} + \frac{1}{2 z^{2}}$$
1/(2*z^2) + log(1 + z)/2 + log(-1 + z)/2 - log(z)
Denominador común
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1 log(1 + z) log(-1 + z) ---- + ---------- + ----------- - log(z) 2 2 2 2*z
$$- \log{\left(z \right)} + \frac{\log{\left(z - 1 \right)}}{2} + \frac{\log{\left(z + 1 \right)}}{2} + \frac{1}{2 z^{2}}$$
1/(2*z^2) + log(1 + z)/2 + log(-1 + z)/2 - log(z)
Denominador racional
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2 2 2
2 - 4*z *log(z) + 2*z *log(1 + z) + 2*z *log(-1 + z)
----------------------------------------------------
2
4*z
$$\frac{- 4 z^{2} \log{\left(z \right)} + 2 z^{2} \log{\left(z - 1 \right)} + 2 z^{2} \log{\left(z + 1 \right)} + 2}{4 z^{2}}$$
(2 - 4*z^2*log(z) + 2*z^2*log(1 + z) + 2*z^2*log(-1 + z))/(4*z^2)
Combinatoria
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2 2 2
1 + z *log(1 + z) + z *log(-1 + z) - 2*z *log(z)
------------------------------------------------
2
2*z
$$\frac{- 2 z^{2} \log{\left(z \right)} + z^{2} \log{\left(z - 1 \right)} + z^{2} \log{\left(z + 1 \right)} + 1}{2 z^{2}}$$
(1 + z^2*log(1 + z) + z^2*log(-1 + z) - 2*z^2*log(z))/(2*z^2)
Potencias
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1 log(1 + z) log(-1 + z) ---- + ---------- + ----------- - log(z) 2 2 2 2*z
$$- \log{\left(z \right)} + \frac{\log{\left(z - 1 \right)}}{2} + \frac{\log{\left(z + 1 \right)}}{2} + \frac{1}{2 z^{2}}$$
1/(2*z^2) + log(1 + z)/2 + log(-1 + z)/2 - log(z)
Compilar la expresión
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1 log(z + 1) log(z - 1) ---- + ---------- + ---------- - log(z) 2 2 2 2*z
$$- \log{\left(z \right)} + \frac{\log{\left(z - 1 \right)}}{2} + \frac{\log{\left(z + 1 \right)}}{2} + \frac{1}{2 z^{2}}$$
1/(2*z^2) + log(z + 1)/2 + log(z - 1)/2 - log(z)
Unión de expresiones racionales
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2
1 + z *(-2*log(z) + log(1 + z) + log(-1 + z))
---------------------------------------------
2
2*z
$$\frac{z^{2} \left(- 2 \log{\left(z \right)} + \log{\left(z - 1 \right)} + \log{\left(z + 1 \right)}\right) + 1}{2 z^{2}}$$
(1 + z^2*(-2*log(z) + log(1 + z) + log(-1 + z)))/(2*z^2)