Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sinh(x)/(sqrt(1-1/cosh(x)^2)*cosh(x)^2)
¿Cómo vas a descomponer esta sinh(x)/(sqrt(1-1/cosh(x)^2)*cosh(x)^2) expresión en fracciones?
Solución
Ha introducido
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sinh(x)
----------------------------
______________
/ 1 2
/ 1 - -------- *cosh (x)
/ 2
\/ cosh (x)
$$\frac{\sinh{\left(x \right)}}{\sqrt{1 - \frac{1}{\cosh^{2}{\left(x \right)}}} \cosh^{2}{\left(x \right)}}$$
sinh(x)/((sqrt(1 - 1/cosh(x)^2)*cosh(x)^2))
Simplificación general
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sinh(x) ---------------------- __________ / 2 2 \/ tanh (x) *cosh (x)
$$\frac{\sinh{\left(x \right)}}{\sqrt{\tanh^{2}{\left(x \right)}} \cosh^{2}{\left(x \right)}}$$
sinh(x)/(sqrt(tanh(x)^2)*cosh(x)^2)
Unión de expresiones racionales
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sinh(x)
------------------------------
_______________
/ 2
/ -1 + cosh (x) 2
/ ------------- *cosh (x)
/ 2
\/ cosh (x)
$$\frac{\sinh{\left(x \right)}}{\sqrt{\frac{\cosh^{2}{\left(x \right)} - 1}{\cosh^{2}{\left(x \right)}}} \cosh^{2}{\left(x \right)}}$$
sinh(x)/(sqrt((-1 + cosh(x)^2)/cosh(x)^2)*cosh(x)^2)
Respuesta numérica
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(1.0 - 1/cosh(x)^2)^(-0.5)*sinh(x)/cosh(x)^2
(1.0 - 1/cosh(x)^2)^(-0.5)*sinh(x)/cosh(x)^2
Parte trigonométrica
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sinh(x) ---------------------- __________ / 2 2 \/ tanh (x) *cosh (x)
$$\frac{\sinh{\left(x \right)}}{\sqrt{\tanh^{2}{\left(x \right)}} \cosh^{2}{\left(x \right)}}$$
sinh(x)/(sqrt(tanh(x)^2)*cosh(x)^2)
Combinatoria
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sinh(x)
--------------------------------------------
_______________________________
/ / 1 \ / 1 \ 2
/ -|1 + -------|*|-1 + -------| *cosh (x)
\/ \ cosh(x)/ \ cosh(x)/
$$\frac{\sinh{\left(x \right)}}{\sqrt{- \left(-1 + \frac{1}{\cosh{\left(x \right)}}\right) \left(1 + \frac{1}{\cosh{\left(x \right)}}\right)} \cosh^{2}{\left(x \right)}}$$
sinh(x)/(sqrt(-(1 + 1/cosh(x))*(-1 + 1/cosh(x)))*cosh(x)^2)