What is the invertible element of the law of composition xy

What is the invertible element of the law of composition? x*y = xy - 3(x+y) + 12

To find the invertible element for: x*y = xy - 3(x+y) + 12 we first need the neutral element.

Now let the neutrla element be N

=> xN - 3( x+ N) + 12 = x

=> xN - 3x - 3N +12 = x

=> xN - 3N = x+ 3x - 12

=> N ( x-3) = 4 ( x- 3)

=> N = 4

Now for the invertible element I

x * I = N = 4

=> xI - 3(x + I) + 12 = 4

=> xI - 3x - 3I + 12 = 4

=> I ( x-3) = 4 - 12 + 3x

=> I (x-3) = 3x - 8

=> I = (3x -8) / (x - 3)

Therefore the invertible element is (3x - 8) / (x-3).