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How do you 1/(2*sqrt(x)*(1+x)) in partial fractions?

An expression to simplify:

The solution

You have entered [src]
       1       
---------------
    ___        
2*\/ x *(1 + x)
$$\frac{1}{2 \sqrt{x} \left(x + 1\right)}$$
1/((2*sqrt(x))*(1 + x))
Fraction decomposition [src]
1/(2*sqrt(x)) - sqrt(x)/(2*(1 + x))
$$- \frac{\sqrt{x}}{2 \left(x + 1\right)} + \frac{1}{2 \sqrt{x}}$$
              ___  
   1        \/ x   
------- - ---------
    ___   2*(1 + x)
2*\/ x             
Expand expression [src]
/   1   \
|-------|
|    ___|
\2*\/ x /
---------
  1 + x  
$$\frac{\frac{1}{2} \frac{1}{\sqrt{x}}}{x + 1}$$
(1/(2*sqrt(x)))/(1 + x)
Common denominator [src]
       1        
----------------
    ___      3/2
2*\/ x  + 2*x   
$$\frac{1}{2 x^{\frac{3}{2}} + 2 \sqrt{x}}$$
1/(2*sqrt(x) + 2*x^(3/2))
Powers [src]
       1       
---------------
  ___          
\/ x *(2 + 2*x)
$$\frac{1}{\sqrt{x} \left(2 x + 2\right)}$$
1/(sqrt(x)*(2 + 2*x))
Numerical answer [src]
0.5*x^(-0.5)/(1.0 + x)
0.5*x^(-0.5)/(1.0 + x)
Rational denominator [src]
     ___   
   \/ x    
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2*x*(1 + x)
$$\frac{\sqrt{x}}{2 x \left(x + 1\right)}$$
sqrt(x)/(2*x*(1 + x))