What is (((n-2)!(n+2)!))/(((n+3)!(n-1)!)) ?

The solution to (((n-2)!(n+2)!))/(((n+3)!(n-1)!)) is 1/((n+3)(n-1))

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simplify (((n-2)!(n+2)!))/(((n+3)!(n-1)!))

simplify

\frac{( ( n - 2 ) ! ( n + 2 ) ! )}{( ( n + 3 ) ! ( n - 1 ) ! )}

\frac{1}{( n + 3 ) ( n - 1 )}

Solution steps

\frac{( n - 2 ) ! ( n + 2 ) !}{( n + 3 ) ! ( n - 1 ) !}

Cancel the factorials:

\frac{n !}{( n + m ) !} = \frac{1}{( n + 1 ) \cdot ( n + 2 ) \dots ( n + m )}

\frac{( n - 2 ) !}{( n - 1 ) !} = \frac{1}{( n - 1 )}

= \frac{( n + 2 ) !}{( n + 3 ) ! ( n - 1 )}

Cancel the factorials:

\frac{n !}{( n + m ) !} = \frac{1}{( n + 1 ) \cdot ( n + 2 ) \dots ( n + m )}

\frac{( n + 2 ) !}{( n + 3 ) !} = \frac{1}{( n + 3 )}

= \frac{1}{( n + 3 ) ( n - 1 )}

\frac{2 sin ^{2} ( x )}{sin ^{2} ( x ) + 2 cos ^{2} ( x )}

3 n + 3

7 \times (- 3) + (- 2) \times (- 13)

(\frac{x}{y} + \frac{y}{2} + \frac{z}{x})^{2}

((\frac{a}{b})^{- 2})^{\frac{3}{4}}

What is (((n-2)!(n+2)!))/(((n+3)!(n-1)!)) ?
The solution to (((n-2)!(n+2)!))/(((n+3)!(n-1)!)) is 1/((n+3)(n-1))