A nice algebra problem

Algebra Level 2

If there is only one solution to the equation ax2+bx+c=0ax^2+bx+c=0, where a,b,c>0;b2;ax1a,b,c>0;b\neq2;ax\neq-1 and xx is the root of the equation, then what is the value of 3b23b2b2+2b+4b2+16b+12b3812(ax+1)?\cfrac{3}{b-2}-\cfrac{3b-2}{b^2+2b+4}-\cfrac{b^2+16b+12}{b^3-8}-\cfrac{1}{2(ax+1)} ?

If this isn't a constant, then give the maximum value of the expression!

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