Who Has The Bulls Eye?

Algebra Level 5

\[\dfrac{x+\sqrt{x^2-1}}{x-\sqrt{x^2-1}}-\dfrac{x-\sqrt{x^2-1}}{x+\sqrt{x^2-1}}=8x\sqrt{x^2-3x+2}\]

How many real values of \(x\) satisfy the above equation?

Note/Hint: Real roots may lead to complex values.

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