Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
exp(x)/sqrt(1-exp(2*x))-exp(2*x)/(sqrt(1-e^(2*x))*sqrt(exp(2*x)))
¿Cómo vas a descomponer esta exp(x)/sqrt(1-exp(2*x))-exp(2*x)/(sqrt(1-e^(2*x))*sqrt(exp(2*x))) expresión en fracciones?
Solución
Ha introducido
[src]
x 2*x
e e
------------- - -----------------------
__________ __________ ______
/ 2*x / 2*x / 2*x
\/ 1 - e \/ 1 - E *\/ e
$$\frac{e^{x}}{\sqrt{1 - e^{2 x}}} - \frac{e^{2 x}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}}$$
exp(x)/sqrt(1 - exp(2*x)) - exp(2*x)/(sqrt(1 - E^(2*x))*sqrt(exp(2*x)))
Simplificación general
[src]
/ ______ \ | / 2*x x| x \\/ e - e /*e ----------------------- __________ ______ / 2*x / 2*x \/ 1 - e *\/ e
$$\frac{\left(- e^{x} + \sqrt{e^{2 x}}\right) e^{x}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}}$$
(sqrt(exp(2*x)) - exp(x))*exp(x)/(sqrt(1 - exp(2*x))*sqrt(exp(2*x)))
Respuesta numérica
[src]
(1.0 - exp(2*x))^(-0.5)*exp(x) - (1.0 - 2.71828182845905^(2.0*x))^(-0.5)*exp(2*x)^(-0.5)*exp(2*x)
(1.0 - exp(2*x))^(-0.5)*exp(x) - (1.0 - 2.71828182845905^(2.0*x))^(-0.5)*exp(2*x)^(-0.5)*exp(2*x)
Compilar la expresión
[src]
x 2*x
e e
------------- - -----------------------
__________ __________ ______
/ 2*x / 2*x / 2*x
\/ 1 - e \/ 1 - e *\/ e
$$- \frac{e^{2 x}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}} + \frac{e^{x}}{\sqrt{1 - e^{2 x}}}$$
exp(x)/sqrt(1 - exp(2*x)) - exp(2*x)/(sqrt(1 - exp(2*x))*sqrt(exp(2*x)))
Denominador común
[src]
/ ______ \
| / 2*x x 2*x|
-\- \/ e *e + e /
-------------------------
__________ ______
/ 2*x / 2*x
\/ 1 - e *\/ e
$$- \frac{e^{2 x} - e^{x} \sqrt{e^{2 x}}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}}$$
-(-sqrt(exp(2*x))*exp(x) + exp(2*x))/(sqrt(1 - exp(2*x))*sqrt(exp(2*x)))
Denominador racional
[src]
/ __________ ______ __________ \
| / 2*x / 2*x 2*x / 2*x x 2*x| -2*x
\\/ 1 - e *\/ e *e - \/ 1 - e *e *e /*e
------------------------------------------------------------
2*x
-1 + e
$$\frac{\left(\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}} e^{2 x} - \sqrt{1 - e^{2 x}} e^{x} e^{2 x}\right) e^{- 2 x}}{e^{2 x} - 1}$$
(sqrt(1 - exp(2*x))*sqrt(exp(2*x))*exp(2*x) - sqrt(1 - exp(2*x))*exp(x)*exp(2*x))*exp(-2*x)/(-1 + exp(2*x))
Potencias
[src]
x 2*x
e e
------------- - -----------------------
__________ __________ ______
/ 2*x / 2*x / 2*x
\/ 1 - e \/ 1 - e *\/ e
$$- \frac{e^{2 x}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}} + \frac{e^{x}}{\sqrt{1 - e^{2 x}}}$$
x 2*x
e e
------------- - --------------------
__________ _________________
/ 2*x / / 2*x\ 2*x
\/ 1 - e \/ \1 - e /*e
$$\frac{e^{x}}{\sqrt{1 - e^{2 x}}} - \frac{e^{2 x}}{\sqrt{\left(1 - e^{2 x}\right) e^{2 x}}}$$
exp(x)/sqrt(1 - exp(2*x)) - exp(2*x)/sqrt((1 - exp(2*x))*exp(2*x))
Unión de expresiones racionales
[src]
/ ______ \ | / 2*x x| x \\/ e - e /*e ----------------------- __________ ______ / 2*x / 2*x \/ 1 - e *\/ e
$$\frac{\left(- e^{x} + \sqrt{e^{2 x}}\right) e^{x}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}}$$
(sqrt(exp(2*x)) - exp(x))*exp(x)/(sqrt(1 - exp(2*x))*sqrt(exp(2*x)))
Parte trigonométrica
[src]
x 2*x
e e
------------- - -----------------------
__________ __________ ______
/ 2*x / 2*x / 2*x
\/ 1 - e \/ 1 - e *\/ e
$$- \frac{e^{2 x}}{\sqrt{1 - e^{2 x}} \sqrt{e^{2 x}}} + \frac{e^{x}}{\sqrt{1 - e^{2 x}}}$$
_______________________
- \/ cosh(2*x) + sinh(2*x) + cosh(x) + sinh(x)
-----------------------------------------------
___________________________
\/ 1 - cosh(2*x) - sinh(2*x)
$$\frac{- \sqrt{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)}} + \sinh{\left(x \right)} + \cosh{\left(x \right)}}{\sqrt{- \sinh{\left(2 x \right)} - \cosh{\left(2 x \right)} + 1}}$$
_______________________
cosh(x) + sinh(x) \/ cosh(2*x) + sinh(2*x)
----------------------------- - -----------------------------
___________________________ ___________________________
\/ 1 - cosh(2*x) - sinh(2*x) \/ 1 - cosh(2*x) - sinh(2*x)
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\sqrt{- \sinh{\left(2 x \right)} - \cosh{\left(2 x \right)} + 1}} - \frac{\sqrt{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)}}}{\sqrt{- \sinh{\left(2 x \right)} - \cosh{\left(2 x \right)} + 1}}$$
_______________________
cosh(x) + sinh(x) \/ cosh(2*x) + sinh(2*x)
----------------------------- - -------------------------------
___________________________ ____________________________
\/ 1 - cosh(2*x) - sinh(2*x) / 2*x
\/ 1 - (cosh(1) + sinh(1))
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\sqrt{- \sinh{\left(2 x \right)} - \cosh{\left(2 x \right)} + 1}} - \frac{\sqrt{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)}}}{\sqrt{1 - \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{2 x}}}$$
(cosh(x) + sinh(x))/sqrt(1 - cosh(2*x) - sinh(2*x)) - sqrt(cosh(2*x) + sinh(2*x))/sqrt(1 - (cosh(1) + sinh(1))^(2*x))
Combinatoria
[src]
/ ______ \
| / 2*x x| x
-\- \/ e + e /*e
----------------------------------
_____________________ ______
/ / x\ / x\ / 2*x
\/ -\1 + e /*\-1 + e / *\/ e
$$- \frac{\left(e^{x} - \sqrt{e^{2 x}}\right) e^{x}}{\sqrt{- \left(e^{x} - 1\right) \left(e^{x} + 1\right)} \sqrt{e^{2 x}}}$$
-(-sqrt(exp(2*x)) + exp(x))*exp(x)/(sqrt(-(1 + exp(x))*(-1 + exp(x)))*sqrt(exp(2*x)))