Factor (Problem below)

Question

2(1+x)^1/2   - x(1+x)^-1/2     

________________________

x+1

 

Confused, help is appreciated.

Answer 1

LET T =1+x = x+1

 

2T^(1/2) - x T ^(-1/2)

-------------------------

      T

 

T^(-1/2)  [   2T - x]

-----------------------

    T

 

2T - x

------------

  T^(3/2)

 

The top is

2(x+1)- x = 2x + 2 - x = x + 2

 

 

  x+2

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(x+1)^(3/2)