Fatorial #6

Algebra Level 2

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

(x!)2(x+2)!(x2)!(x+1)!(x1)!(x!)2=f(x)g(x). \frac{(x!)^2 (x + 2)! (x - 2)!}{(x + 1)! (x - 1)! (x!)^2} = \frac{ f(x) } { g( x) }.

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

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

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