Sr Examen
¿Cómo vas a descomponer esta Ctg1/(a*x-1)-1/(a*x+1) expresión en fracciones?
Solución
Ha introducido
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cot(1) 1 ------- - ------- a*x - 1 a*x + 1
$$- \frac{1}{a x + 1} + \frac{\cot{\left(1 \right)}}{a x - 1}$$
cot(1)/(a*x - 1) - 1/(a*x + 1)
Simplificación general
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1 + (1 + a*x)*cot(1) - a*x -------------------------- (1 + a*x)*(-1 + a*x)
$$\frac{- a x + \left(a x + 1\right) \cot{\left(1 \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)}$$
(1 + (1 + a*x)*cot(1) - a*x)/((1 + a*x)*(-1 + a*x))
Respuesta numérica
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-1/(1.0 + a*x) + 0.642092615934331/(-1.0 + a*x)
-1/(1.0 + a*x) + 0.642092615934331/(-1.0 + a*x)
Combinatoria
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1 - a*x + a*x*cot(1) + cot(1)
-----------------------------
(1 + a*x)*(-1 + a*x)
$$\frac{- a x + a x \cot{\left(1 \right)} + \cot{\left(1 \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)}$$
(1 - a*x + a*x*cot(1) + cot(1))/((1 + a*x)*(-1 + a*x))
Denominador común
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1 - a*x + a*x*cot(1) + cot(1)
-----------------------------
2 2
-1 + a *x
$$\frac{- a x + a x \cot{\left(1 \right)} + \cot{\left(1 \right)} + 1}{a^{2} x^{2} - 1}$$
(1 - a*x + a*x*cot(1) + cot(1))/(-1 + a^2*x^2)
Unión de expresiones racionales
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1 + (1 + a*x)*cot(1) - a*x -------------------------- (1 + a*x)*(-1 + a*x)
$$\frac{- a x + \left(a x + 1\right) \cot{\left(1 \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)}$$
(1 + (1 + a*x)*cot(1) - a*x)/((1 + a*x)*(-1 + a*x))
Parte trigonométrica
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1 csc(1)
- ------- + -----------------------
1 + a*x / pi\
(-1 + a*x)*csc|-1 + --|
\ 2 /
$$- \frac{1}{a x + 1} + \frac{\csc{\left(1 \right)}}{\left(a x - 1\right) \csc{\left(-1 + \frac{\pi}{2} \right)}}$$
1 csc(1) - ------- + ----------------- 1 + a*x (-1 + a*x)*sec(1)
$$- \frac{1}{a x + 1} + \frac{\csc{\left(1 \right)}}{\left(a x - 1\right) \sec{\left(1 \right)}}$$
/ pi\
sec|1 - --|
1 \ 2 /
- ------- + -----------------
1 + a*x (-1 + a*x)*sec(1)
$$- \frac{1}{a x + 1} + \frac{\sec{\left(1 - \frac{\pi}{2} \right)}}{\left(a x - 1\right) \sec{\left(1 \right)}}$$
1 sin(2)
- ------- + --------------------
1 + a*x 2
2*(-1 + a*x)*sin (1)
$$- \frac{1}{a x + 1} + \frac{\sin{\left(2 \right)}}{2 \left(a x - 1\right) \sin^{2}{\left(1 \right)}}$$
1 cos(1)
- ------- + ----------------------
1 + a*x / pi\
(-1 + a*x)*cos|1 - --|
\ 2 /
$$- \frac{1}{a x + 1} + \frac{\cos{\left(1 \right)}}{\left(a x - 1\right) \cos{\left(1 - \frac{\pi}{2} \right)}}$$
1 1 - ------- + ----------------- 1 + a*x (-1 + a*x)*tan(1)
$$- \frac{1}{a x + 1} + \frac{1}{\left(a x - 1\right) \tan{\left(1 \right)}}$$
1 cos(1) - ------- + ----------------- 1 + a*x (-1 + a*x)*sin(1)
$$- \frac{1}{a x + 1} + \frac{\cos{\left(1 \right)}}{\left(a x - 1\right) \sin{\left(1 \right)}}$$
-1/(1 + a*x) + cos(1)/((-1 + a*x)*sin(1))
Denominador racional
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1 + (1 + a*x)*cot(1) - a*x -------------------------- (1 + a*x)*(-1 + a*x)
$$\frac{- a x + \left(a x + 1\right) \cot{\left(1 \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)}$$
(1 + (1 + a*x)*cot(1) - a*x)/((1 + a*x)*(-1 + a*x))