Fatorial #6

Algebra Level 2

\(f(x) \) and \(g(x) \) are algebraic expressions such that

\[ \frac{(x!)^2 (x + 2)! (x - 2)!}{(x + 1)! (x - 1)! (x!)^2} = \frac{ f(x) } { g( x) }. \]

What is \( f(x) - g(x) ? \)

Note: \(\frac{ f(x) } { g(x) } \) should be simplified to an irreducible positive fraction.

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