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Find all real values of $x$ such that
\frac{x^2 + 2x + 5}{3x^2 - x - 4} + \frac{x^2 + 4x + 8}{x^2 - 4x - 5}  \ge 0.

Note: Your solution should be thorough, and explain why all your values are the only values that satisfy the inequality.

 Nov 21, 2023

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