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Simplificación de expresiones/ Descomposición en fracciones simples/ atan((4*x-2)/(2*sqrt(5)))/sqrt(5)

¿Cómo vas a descomponer esta atan((4*x-2)/(2*sqrt(5)))/sqrt(5) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    /4*x - 2\
atan|-------|
    |    ___|
    \2*\/ 5 /
-------------
      ___    
    \/ 5
$$\frac{\operatorname{atan}{\left(\frac{4 x - 2}{2 \sqrt{5}} \right)}}{\sqrt{5}}$$ 
atan((4*x - 2)/((2*sqrt(5))))/sqrt(5)
Descomposición de una fracción [src] 
sqrt(5)*atan(-sqrt(5)/5 + 2*x*sqrt(5)/5)/5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{2 \sqrt{5} x}{5} - \frac{\sqrt{5}}{5} \right)}}{5}$$ 
          /    ___         ___\
  ___     |  \/ 5    2*x*\/ 5 |
\/ 5 *atan|- ----- + ---------|
          \    5         5    /
-------------------------------
               5
Simplificación general [src] 
          /  ___           \
  ___     |\/ 5 *(-1 + 2*x)|
\/ 5 *atan|----------------|
          \       5        /
----------------------------
             5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 x - 1\right)}{5} \right)}}{5}$$ 
sqrt(5)*atan(sqrt(5)*(-1 + 2*x)/5)/5
Respuesta numérica [src] 
0.447213595499958*atan((4*x - 2)/((2*sqrt(5))))
0.447213595499958*atan((4*x - 2)/((2*sqrt(5))))
Unión de expresiones racionales [src] 
          /  ___           \
  ___     |\/ 5 *(-1 + 2*x)|
\/ 5 *atan|----------------|
          \       5        /
----------------------------
             5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 x - 1\right)}{5} \right)}}{5}$$ 
sqrt(5)*atan(sqrt(5)*(-1 + 2*x)/5)/5
Combinatoria [src] 
          /    ___         ___\
  ___     |  \/ 5    2*x*\/ 5 |
\/ 5 *atan|- ----- + ---------|
          \    5         5    /
-------------------------------
               5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{2 \sqrt{5} x}{5} - \frac{\sqrt{5}}{5} \right)}}{5}$$ 
sqrt(5)*atan(-sqrt(5)/5 + 2*x*sqrt(5)/5)/5
Denominador común [src] 
          /    ___         ___\
  ___     |  \/ 5    2*x*\/ 5 |
\/ 5 *atan|- ----- + ---------|
          \    5         5    /
-------------------------------
               5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{2 \sqrt{5} x}{5} - \frac{\sqrt{5}}{5} \right)}}{5}$$ 
sqrt(5)*atan(-sqrt(5)/5 + 2*x*sqrt(5)/5)/5
Parte trigonométrica [src] 
          /  ___           \
  ___     |\/ 5 *(-2 + 4*x)|
\/ 5 *atan|----------------|
          \       10       /
----------------------------
             5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(4 x - 2\right)}{10} \right)}}{5}$$ 
sqrt(5)*atan(sqrt(5)*(-2 + 4*x)/10)/5
Compilar la expresión [src] 
  ___     /4*x - 2\
\/ 5 *atan|-------|
          |    ___|
          \2*\/ 5 /
-------------------
         5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{4 x - 2}{2 \sqrt{5}} \right)}}{5}$$ 
sqrt(5)*atan((4*x - 2)/((2*sqrt(5))))/5
Denominador racional [src] 
          /  ___           \
  ___     |\/ 5 *(-1 + 2*x)|
\/ 5 *atan|----------------|
          \       5        /
----------------------------
             5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 x - 1\right)}{5} \right)}}{5}$$ 
sqrt(5)*atan(sqrt(5)*(-1 + 2*x)/5)/5
Abrimos la expresión [src] 
  ___     /  ___          \
\/ 5      |\/ 5 *(4*x - 2)|
-----*atan|---------------|
  5       \       10      /
$$\frac{\sqrt{5}}{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(4 x - 2\right)}{10} \right)}$$ 
(sqrt(5)/5)*atan(sqrt(5)*(4*x - 2)/10)
Potencias [src] 
          /  ___           \
  ___     |\/ 5 *(-2 + 4*x)|
\/ 5 *atan|----------------|
          \       10       /
----------------------------
             5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(4 x - 2\right)}{10} \right)}}{5}$$ 
  ___     /  ___ /  1   2*x\\
\/ 5 *atan|\/ 5 *|- - + ---||
          \      \  5    5 //
-----------------------------
              5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\sqrt{5} \left(\frac{2 x}{5} - \frac{1}{5}\right) \right)}}{5}$$ 
sqrt(5)*atan(sqrt(5)*(-1/5 + 2*x/5))/5
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