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Expression simplification/ Fraction Decomposition into the simple/ (e^(3x)+1)/(e^x+1)

How do you (e^(3x)+1)/(e^x+1) in partial fractions?

An expression to simplify:

The solution

You have entered [src] 
 3*x    
E    + 1
--------
  x     
 E  + 1
$$\frac{e^{3 x} + 1}{e^{x} + 1}$$ 
(E^(3*x) + 1)/(E^x + 1)
General simplification [src] 
     x    2*x
1 - e  + e
$$e^{2 x} - e^{x} + 1$$ 
1 - exp(x) + exp(2*x)
Fraction decomposition [src] 
1 - exp(x) + exp(2*x)
$$e^{2 x} - e^{x} + 1$$ 
     x    2*x
1 - e  + e
Numerical answer [src] 
(1.0 + 2.71828182845905^(3.0*x))/(1.0 + 2.71828182845905^x)
(1.0 + 2.71828182845905^(3.0*x))/(1.0 + 2.71828182845905^x)
Combinatorics [src] 
     x    2*x
1 - e  + e
$$e^{2 x} - e^{x} + 1$$ 
1 - exp(x) + exp(2*x)
Common denominator [src] 
     x    2*x
1 - e  + e
$$e^{2 x} - e^{x} + 1$$ 
1 - exp(x) + exp(2*x)
Trigonometric part [src] 
1 + cosh(3*x) + sinh(3*x)
-------------------------
  1 + cosh(x) + sinh(x)
$$\frac{\sinh{\left(3 x \right)} + \cosh{\left(3 x \right)} + 1}{\sinh{\left(x \right)} + \cosh{\left(x \right)} + 1}$$ 
                       3*x
1 + (cosh(1) + sinh(1))   
--------------------------
                        x 
 1 + (cosh(1) + sinh(1))
$$\frac{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{3 x} + 1}{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} + 1}$$ 
                       2*x                      x
1 + (cosh(1) + sinh(1))    - (cosh(1) + sinh(1))
$$\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{2 x} - \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} + 1$$ 
1 + (cosh(1) + sinh(1))^(2*x) - (cosh(1) + sinh(1))^x
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