# Solve for: (2 * (n+2) !)/((n+1) !)=12

## Expression: $\frac{ 2 \times \left( n+2 \right) ! }{ \left( n+1 \right) ! }=12$

Use $n !=n \times \left( n-1 \right) !$ to expand the expression

$\frac{ 2\left( n+2 \right) \times \left( n+1 \right) ! }{ \left( n+1 \right) ! }=12$

Cancel out the common factor $\left( n+1 \right) !$

$2\left( n+2 \right)=12$

Divide both sides of the equation by $2$

$n+2=6$

Move the constant to the right-hand side and change its sign

$n=6-2$

Subtract the numbers

$n=4$

Check if the given value is the solution of the equation

$\frac{ 2 \times \left( 4+2 \right) ! }{ \left( 4+1 \right) ! }=12$

Simplify the expression

$12=12$

The equality is true, therefore $n=4$ is a solution of the equation

$n=4$

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