Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(a)^(2)-sin(1)/(a*x-1)-1/(a*x+1)
¿Cómo vas a descomponer esta tan(a)^(2)-sin(1)/(a*x-1)-1/(a*x+1) expresión en fracciones?
Solución
Ha introducido
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2 sin(1) 1
tan (a) - ------- - -------
a*x - 1 a*x + 1
$$\left(\tan^{2}{\left(a \right)} - \frac{\sin{\left(1 \right)}}{a x - 1}\right) - \frac{1}{a x + 1}$$
tan(a)^2 - sin(1)/(a*x - 1) - 1/(a*x + 1)
Simplificación general
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2 1 sin(1)
tan (a) - ------- - --------
1 + a*x -1 + a*x
$$\tan^{2}{\left(a \right)} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1}$$
tan(a)^2 - 1/(1 + a*x) - sin(1)/(-1 + a*x)
Respuesta numérica
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tan(a)^2 - 1/(1.0 + a*x) - 0.841470984807897/(-1.0 + a*x)
tan(a)^2 - 1/(1.0 + a*x) - 0.841470984807897/(-1.0 + a*x)
Denominador racional
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/ 2 \
1 + (1 + a*x)*\-sin(1) + tan (a)*(-1 + a*x)/ - a*x
--------------------------------------------------
(1 + a*x)*(-1 + a*x)
$$\frac{- a x + \left(a x + 1\right) \left(\left(a x - 1\right) \tan^{2}{\left(a \right)} - \sin{\left(1 \right)}\right) + 1}{\left(a x - 1\right) \left(a x + 1\right)}$$
(1 + (1 + a*x)*(-sin(1) + tan(a)^2*(-1 + a*x)) - a*x)/((1 + a*x)*(-1 + a*x))
Unión de expresiones racionales
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/ 2 \
1 + (1 + a*x)*\-sin(1) + tan (a)*(-1 + a*x)/ - a*x
--------------------------------------------------
(1 + a*x)*(-1 + a*x)
$$\frac{- a x + \left(a x + 1\right) \left(\left(a x - 1\right) \tan^{2}{\left(a \right)} - \sin{\left(1 \right)}\right) + 1}{\left(a x - 1\right) \left(a x + 1\right)}$$
(1 + (1 + a*x)*(-sin(1) + tan(a)^2*(-1 + a*x)) - a*x)/((1 + a*x)*(-1 + a*x))
Denominador común
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2 -1 + a*x + a*x*sin(1) + sin(1)
tan (a) - ------------------------------
2 2
-1 + a *x
$$\tan^{2}{\left(a \right)} - \frac{a x \sin{\left(1 \right)} + a x - 1 + \sin{\left(1 \right)}}{a^{2} x^{2} - 1}$$
tan(a)^2 - (-1 + a*x + a*x*sin(1) + sin(1))/(-1 + a^2*x^2)
Potencias
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2 1 sin(1)
tan (a) - ------- - --------
1 + a*x -1 + a*x
$$\tan^{2}{\left(a \right)} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1}$$
2
/ I*a -I*a\ / -I I\
1 \- e + e / I*\- e + e /
- ------- - ----------------- + --------------
1 + a*x 2 2*(-1 + a*x)
/ I*a -I*a\
\e + e /
$$- \frac{\left(- e^{i a} + e^{- i a}\right)^{2}}{\left(e^{i a} + e^{- i a}\right)^{2}} - \frac{1}{a x + 1} + \frac{i \left(- e^{- i} + e^{i}\right)}{2 \left(a x - 1\right)}$$
-1/(1 + a*x) - (-exp(i*a) + exp(-i*a))^2/(exp(i*a) + exp(-i*a))^2 + i*(-exp(-i) + exp(i))/(2*(-1 + a*x))
Compilar la expresión
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2 1 sin(1)
tan (a) - ------- - --------
1 + a*x -1 + a*x
$$\tan^{2}{\left(a \right)} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1}$$
tan(a)^2 - 1/(1 + a*x) - sin(1)/(-1 + a*x)
Combinatoria
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2 2 2 2
1 - tan (a) - sin(1) - a*x + a *x *tan (a) - a*x*sin(1)
-------------------------------------------------------
(1 + a*x)*(-1 + a*x)
$$\frac{a^{2} x^{2} \tan^{2}{\left(a \right)} - a x - a x \sin{\left(1 \right)} - \tan^{2}{\left(a \right)} - \sin{\left(1 \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)}$$
(1 - tan(a)^2 - sin(1) - a*x + a^2*x^2*tan(a)^2 - a*x*sin(1))/((1 + a*x)*(-1 + a*x))
Parte trigonométrica
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2 1 sin(1)
tan (a) - ------- - --------
1 + a*x -1 + a*x
$$\tan^{2}{\left(a \right)} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1}$$
2 1 sin(1)
tan (a) - ------- - -------
a*x + 1 a*x - 1
$$\tan^{2}{\left(a \right)} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1}$$
2/pi \
csc |-- - a|
1 \2 / 1
- ------- + ------------ - -----------------
1 + a*x 2 (-1 + a*x)*csc(1)
csc (a)
$$\frac{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(a \right)}} - \frac{1}{a x + 1} - \frac{1}{\left(a x - 1\right) \csc{\left(1 \right)}}$$
2 1 2*tan(1/2)
tan (a) - ------- - --------------------------
1 + a*x / 2 \
\1 + tan (1/2)/*(-1 + a*x)
$$\tan^{2}{\left(a \right)} - \frac{1}{a x + 1} - \frac{2 \tan{\left(\frac{1}{2} \right)}}{\left(a x - 1\right) \left(\tan^{2}{\left(\frac{1}{2} \right)} + 1\right)}$$
1 1 2*cot(1/2) ------- - ------- - -------------------------- 2 1 + a*x / 2 \ cot (a) \1 + cot (1/2)/*(-1 + a*x)
$$\frac{1}{\cot^{2}{\left(a \right)}} - \frac{1}{a x + 1} - \frac{2 \cot{\left(\frac{1}{2} \right)}}{\left(1 + \cot^{2}{\left(\frac{1}{2} \right)}\right) \left(a x - 1\right)}$$
4
1 sin(1) 4*sin (a)
- ------- - -------- + ---------
1 + a*x -1 + a*x 2
sin (2*a)
$$\frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1}$$
2
1 sin (a) sin(1)
- ------- + ------- - --------
1 + a*x 2 -1 + a*x
cos (a)
$$\frac{\sin^{2}{\left(a \right)}}{\cos^{2}{\left(a \right)}} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1}$$
2
1 sec (a) 1
- ------- + ------- - -----------------
1 + a*x 2 (-1 + a*x)*csc(1)
csc (a)
$$\frac{\sec^{2}{\left(a \right)}}{\csc^{2}{\left(a \right)}} - \frac{1}{a x + 1} - \frac{1}{\left(a x - 1\right) \csc{\left(1 \right)}}$$
2
1 sec (a) 1
- ------- + ------------ - ----------------------
1 + a*x 2/ pi\ / pi\
sec |a - --| (-1 + a*x)*sec|1 - --|
\ 2 / \ 2 /
$$\frac{\sec^{2}{\left(a \right)}}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} - \frac{1}{a x + 1} - \frac{1}{\left(a x - 1\right) \sec{\left(1 - \frac{\pi}{2} \right)}}$$
2/ pi\ / pi\
cos |a - --| cos|1 - --|
1 \ 2 / \ 2 /
- ------- + ------------ - -----------
1 + a*x 2 -1 + a*x
cos (a)
$$\frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a \right)}} - \frac{1}{a x + 1} - \frac{\cos{\left(1 - \frac{\pi}{2} \right)}}{a x - 1}$$
-1/(1 + a*x) + cos(a - pi/2)^2/cos(a)^2 - cos(1 - pi/2)/(-1 + a*x)