What is the answer to (n!)/((n+1)!)=12 ?

The answer to (n!)/((n+1)!)=12 is n=-11/12

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(n!)/((n+1)!)=12

\frac{n !}{( n + 1 ) !} = 12

n = - \frac{11}{12}

Decimal Notation

n = - 0.91666 \dots

Solution steps

\frac{n !}{( n + 1 ) !} = 12

Simplify

\frac{n !}{( n + 1 ) !} : \frac{1}{n + 1}

\frac{1}{n + 1} = 12

Multiply both sides by

n + 1

1 = 12 (n + 1)

Switch sides

12 (n + 1) = 1

Divide both sides by

12

n + 1 = \frac{1}{12}

Move

1

to the right side

n = - \frac{11}{12}

\frac{5 x ^{2} + 1}{x} = 6

\frac{( x ^{2} + 5 x + 6 )}{( x + 3 )} = x + 7

\frac{( x + 1 ) ^{2}}{( ( x + 2 ) ^{2} )} = \frac{( x + 2 )}{( x + 4 )}

x^{- 3} = 8

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

What is the answer to (n!)/((n+1)!)=12 ?
The answer to (n!)/((n+1)!)=12 is n=-11/12
Solve for n: (n!)/((n+1)!)=12
The solution is n=-11/12