# Will it even end?

Algebra Level 4

$\dfrac{1}{x-1}-\dfrac{4}{x-2}+\dfrac{4}{x-3}-\dfrac{1}{x-4} < \dfrac{1}{30}$

If the range of $$x$$ satisfying the above inequality is in the form as given below.

$(-\infty,a)\cup (b,c)\cup (d,e) \cup (f,g) \cup (h,\infty)$

Find $$a+b+c+d+e+f+g+h$$.

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