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¿Cómo vas a descomponer esta sign(atan(x-2))/(1+(x-2)^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
sign(atan(x - 2))
-----------------
              2  
   1 + (x - 2)   
$$\frac{\operatorname{sign}{\left(\operatorname{atan}{\left(x - 2 \right)} \right)}}{\left(x - 2\right)^{2} + 1}$$
sign(atan(x - 2))/(1 + (x - 2)^2)
Denominador racional [src]
sign(atan(-2 + x))
------------------
        2         
   5 + x  - 4*x   
$$\frac{\operatorname{sign}{\left(\operatorname{atan}{\left(x - 2 \right)} \right)}}{x^{2} - 4 x + 5}$$
sign(atan(-2 + x))/(5 + x^2 - 4*x)
Combinatoria [src]
sign(atan(-2 + x))
------------------
        2         
   5 + x  - 4*x   
$$\frac{\operatorname{sign}{\left(\operatorname{atan}{\left(x - 2 \right)} \right)}}{x^{2} - 4 x + 5}$$
sign(atan(-2 + x))/(5 + x^2 - 4*x)
Denominador común [src]
sign(atan(-2 + x))
------------------
        2         
   5 + x  - 4*x   
$$\frac{\operatorname{sign}{\left(\operatorname{atan}{\left(x - 2 \right)} \right)}}{x^{2} - 4 x + 5}$$
sign(atan(-2 + x))/(5 + x^2 - 4*x)
Respuesta numérica [src]
sign(atan(x - 2))/(1.0 + 4.0*(-1 + 0.5*x)^2)
sign(atan(x - 2))/(1.0 + 4.0*(-1 + 0.5*x)^2)