Question 77150
4/2x+6 - 3/x+3 = x/2 
Rewrite as:
2/(x+3) - 3/(x+3) = x/2

Multiply thru by 2(x+3) to get:

4 -6 = x^2+3x
x^2+3x+2=0
(x+2)(x+1)=0
x=-2 or x=-1

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cheers,
Stan H.