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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             
Rational denominator [src]
     ___   
  -\/ x    
-----------
2*x*(1 + x)
$$- \frac{\sqrt{x}}{2 x \left(x + 1\right)}$$
-sqrt(x)/(2*x*(1 + x))
Numerical answer [src]
-0.5*x^(-0.5)/(1.0 + x)
-0.5*x^(-0.5)/(1.0 + x)
Powers [src]
      -1       
---------------
  ___          
\/ x *(2 + 2*x)
$$- \frac{1}{\sqrt{x} \left(2 x + 2\right)}$$
-1/(sqrt(x)*(2 + 2*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))