What is expand ((3x)!)/((3(x+1))!) ?

The solution to expand ((3x)!)/((3(x+1))!) is 1/(27x^3+54x^2+33x+6)

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expand ((3x)!)/((3(x+1))!)

expand

\frac{( 3 x ) !}{( 3 ( x + 1 ) ) !}

\frac{1}{27 x ^{3} + 54 x ^{2} + 33 x + 6}

Solution steps

\frac{( 3 x ) !}{( 3 ( x + 1 ) ) !}

Cancel the factorials:

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

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

= \frac{1}{3 ( x + 1 ) ( 3 x + 2 ) ( 3 x + 1 )}

Expand

3 (x + 1) (3 x + 2) (3 x + 1) : 27 x^{3} + 54 x^{2} + 33 x + 6

= \frac{1}{27 x ^{3} + 54 x ^{2} + 33 x + 6}

\frac{1 + 3 x}{( 1 + 2 x ) ^{3}}

\frac{8}{( s + 1 ) ( s ^{2} + 4 )}

\frac{ln ( ( x - 7 ) ( x - 9 ) )}{ln ( a x + b )}

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

\frac{2}{( s + 1 ) \cdot ( s + 2 )}

What is expand ((3x)!)/((3(x+1))!) ?
The solution to expand ((3x)!)/((3(x+1))!) is 1/(27x^3+54x^2+33x+6)