# They call it logarithms?

Algebra Level 5

$\large \log_{\frac{3x}{x^2+1}} \left(x^2-\frac{5}{2}x+1\right) \geq 0$

If the range of $$x$$ satisfying the above inequality is in the form $$(a,b) \cup [c,d)$$, then find $$a+b+c+d$$ where $$a,b,c,d \in \mathbb{R}$$.

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