# A nice algebra problem

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

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

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