Brush up your fundamentals 1

Algebra Level 5

\[\left|\dfrac{x-1}{3 + 2x - 8x^{2}}\right| + \left| 1 - x \right| = \dfrac{(x -1)^{2}}{\left| 3+ 2x -8x^{2}\right|} + 1\]

The solutions to the equation are of the form

\[x = a , b , \dfrac{c \pm \sqrt{d}}{e} , \dfrac{ f \pm \sqrt{g}}{h}\]

where \(a,b,c,d,e,f,g,h\) are all positive integers, with \(d\) and \(g\) square-free.

Find the value of \(a + b + c +d+e+f+g+ h\).

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