Sr Examen

Otras calculadoras

¿Cómo vas a descomponer esta tan(x/4+pi/8)/2-1/(2*tan(x/4+pi/8)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
   /x   pi\                
tan|- + --|                
   \4   8 /         1      
----------- - -------------
     2             /x   pi\
              2*tan|- + --|
                   \4   8 /
$$\frac{\tan{\left(\frac{x}{4} + \frac{\pi}{8} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{x}{4} + \frac{\pi}{8} \right)}}$$
tan(x/4 + pi/8)/2 - 1/(2*tan(x/4 + pi/8))
Descomposición de una fracción [src]
tan(x/4 + pi/8)/2 - 1/(2*tan(x/4 + pi/8))
$$\frac{\tan{\left(\frac{x}{4} + \frac{\pi}{8} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{x}{4} + \frac{\pi}{8} \right)}}$$
   /x   pi\                
tan|- + --|                
   \4   8 /         1      
----------- - -------------
     2             /x   pi\
              2*tan|- + --|
                   \4   8 /
Denominador racional [src]
          2/pi   x\
-2 + 2*tan |-- + -|
           \8    4/
-------------------
        /pi   x\   
   4*tan|-- + -|   
        \8    4/   
$$\frac{2 \tan^{2}{\left(\frac{x}{4} + \frac{\pi}{8} \right)} - 2}{4 \tan{\left(\frac{x}{4} + \frac{\pi}{8} \right)}}$$
(-2 + 2*tan(pi/8 + x/4)^2)/(4*tan(pi/8 + x/4))
Potencias [src]
   /   /  x   pi\      /x   pi\\      /     /x   pi\      /  x   pi\\
   | I*|- - - --|    I*|- + --||      |   I*|- + --|    I*|- - - --||
   |   \  4   8 /      \4   8 /|      |     \4   8 /      \  4   8 /|
 I*\e             + e          /    I*\- e           + e            /
--------------------------------- + ---------------------------------
  /     /x   pi\      /  x   pi\\      /   /  x   pi\      /x   pi\\ 
  |   I*|- + --|    I*|- - - --||      | I*|- - - --|    I*|- + --|| 
  |     \4   8 /      \  4   8 /|      |   \  4   8 /      \4   8 /| 
2*\- e           + e            /    2*\e             + e          / 
$$\frac{i \left(e^{i \left(- \frac{x}{4} - \frac{\pi}{8}\right)} - e^{i \left(\frac{x}{4} + \frac{\pi}{8}\right)}\right)}{2 \left(e^{i \left(- \frac{x}{4} - \frac{\pi}{8}\right)} + e^{i \left(\frac{x}{4} + \frac{\pi}{8}\right)}\right)} + \frac{i \left(e^{i \left(- \frac{x}{4} - \frac{\pi}{8}\right)} + e^{i \left(\frac{x}{4} + \frac{\pi}{8}\right)}\right)}{2 \left(e^{i \left(- \frac{x}{4} - \frac{\pi}{8}\right)} - e^{i \left(\frac{x}{4} + \frac{\pi}{8}\right)}\right)}$$
i*(exp(i*(-x/4 - pi/8)) + exp(i*(x/4 + pi/8)))/(2*(-exp(i*(x/4 + pi/8)) + exp(i*(-x/4 - pi/8)))) + i*(-exp(i*(x/4 + pi/8)) + exp(i*(-x/4 - pi/8)))/(2*(exp(i*(-x/4 - pi/8)) + exp(i*(x/4 + pi/8))))
Abrimos la expresión [src]
                                                                                                           /x\                          /x\                   ___    /x\     
                                                                          ___                           tan|-|                       tan|-|                 \/ 2 *tan|-|     
                1                            1                          \/ 2                               \4/                          \4/                          \4/     
- ----------------------------- - ----------------------- + ----------------------------- + ----------------------------- - ----------------------- + -----------------------
    /      ___    /x\      /x\\     /       ___      /x\\     /      ___    /x\      /x\\     /      ___    /x\      /x\\     /       ___      /x\\     /       ___      /x\\
  2*|1 - \/ 2 *tan|-| + tan|-||   2*|-1 + \/ 2  + tan|-||   2*|1 - \/ 2 *tan|-| + tan|-||   2*|1 - \/ 2 *tan|-| + tan|-||   2*|-1 + \/ 2  + tan|-||   2*|-1 + \/ 2  + tan|-||
    \             \4/      \4//     \                \4//     \             \4/      \4//     \             \4/      \4//     \                \4//     \                \4//
$$- \frac{\tan{\left(\frac{x}{4} \right)}}{2 \left(\tan{\left(\frac{x}{4} \right)} - 1 + \sqrt{2}\right)} + \frac{\sqrt{2} \tan{\left(\frac{x}{4} \right)}}{2 \left(\tan{\left(\frac{x}{4} \right)} - 1 + \sqrt{2}\right)} - \frac{1}{2 \left(\tan{\left(\frac{x}{4} \right)} - 1 + \sqrt{2}\right)} + \frac{\tan{\left(\frac{x}{4} \right)}}{2 \left(- \sqrt{2} \tan{\left(\frac{x}{4} \right)} + \tan{\left(\frac{x}{4} \right)} + 1\right)} - \frac{1}{2 \left(- \sqrt{2} \tan{\left(\frac{x}{4} \right)} + \tan{\left(\frac{x}{4} \right)} + 1\right)} + \frac{\sqrt{2}}{2 \left(- \sqrt{2} \tan{\left(\frac{x}{4} \right)} + \tan{\left(\frac{x}{4} \right)} + 1\right)}$$
-1/(2*(1 - sqrt(2)*tan(x/4) + tan(x/4))) - 1/(2*(-1 + sqrt(2) + tan(x/4))) + sqrt(2)/(2*(1 - sqrt(2)*tan(x/4) + tan(x/4))) + tan(x/4)/(2*(1 - sqrt(2)*tan(x/4) + tan(x/4))) - tan(x/4)/(2*(-1 + sqrt(2) + tan(x/4))) + sqrt(2)*tan(x/4)/(2*(-1 + sqrt(2) + tan(x/4)))
Unión de expresiones racionales [src]
        2/pi + 2*x\
-1 + tan |--------|
         \   8    /
-------------------
       /pi + 2*x\  
  2*tan|--------|  
       \   8    /  
$$\frac{\tan^{2}{\left(\frac{2 x + \pi}{8} \right)} - 1}{2 \tan{\left(\frac{2 x + \pi}{8} \right)}}$$
(-1 + tan((pi + 2*x)/8)^2)/(2*tan((pi + 2*x)/8))
Respuesta numérica [src]
0.5*tan(x/4 + pi/8) - 0.5/tan(x/4 + pi/8)
0.5*tan(x/4 + pi/8) - 0.5/tan(x/4 + pi/8)
Combinatoria [src]
/       /x   pi\\ /        /x   pi\\
|1 + tan|- + --||*|-1 + tan|- + --||
\       \4   8 // \        \4   8 //
------------------------------------
                /x   pi\            
           2*tan|- + --|            
                \4   8 /            
$$\frac{\left(\tan{\left(\frac{x}{4} + \frac{\pi}{8} \right)} - 1\right) \left(\tan{\left(\frac{x}{4} + \frac{\pi}{8} \right)} + 1\right)}{2 \tan{\left(\frac{x}{4} + \frac{\pi}{8} \right)}}$$
(1 + tan(x/4 + pi/8))*(-1 + tan(x/4 + pi/8))/(2*tan(x/4 + pi/8))