A Very Nice Math Olympiad Problem | Solve for all values of x

[@paulortega5317]

Or re-arrange to
1/x² = 1/(x + 1)² + 1/(x - 1)²
1/x² = 2(x² + 1)/[(x + 1)²(x - 1)²] = 2(x² + 1)/(x² - 1)²
(x² - 1)² = 2x²(x² + 1)
x⁴ + 4x² - 1 = 0 etc.

[@SpencersAcademy]

Nice one 👍

[@ayebaemiwilson4360]

Why don't you use "difference of two square"?

[@JudithSweeney-p1o]

He did, in rationalizing the denominator.