Question

X= an+2/n+1
Make n the subject

Answer 1

n x = a n^2 + n + 2

a n^2+(1-x)n + 2 = 0

n= [ -a +/- sqrt (1-2x+x^2 -8a) ] / 2a

Answer 2

If your question means:

x = ( a n + 2 ) / ( n + 1 )

then

Multiply both sides by n + 1

x ( n + 1 ) = ( a n + 2 )

x n + x = a n + 2

Subtract x to both sides

x n = a n + 2 - x

Subttract a n to both sides

x n - a n = 2 - x

n ( x - a ) = 2 - x

Divide both sides by x - a

n = ( 2 - x ) / ( x - a )

Multiply numerator and denominator by - 1

x = ( x - 2 ) / ( a - x )

Answer 3

I make typo in last step.

The solution is:

n = ( x - 2 ) / ( a - x )