# 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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