Let's simplify the given expression step by step:

(3c+6) = 3c + 6

(c#c-c-3) = c^2 - c - c - 3 = c^2 - 2c - 3

(c#c-4) = c^2 - 4

Now, substitute these values back into the expression:

3c + 6 + (c^2 - 2c - 3): (c^2 - 4) - 1

Now, simplify the division operation first:

= 3c + 6 + (c^2 - 2c - 3) / (c^2 - 4) - 1

Now combine like terms:

= 3c + 6 + (c^2 - 2c - 3) / (c^2 - 4) - 1

Now perform division:

= 3c + 6 + (c^2 - 2c - 3) / (c^2 - 4) - 1

Therefore, the final simplified expression is 3c + 6 + (c^2 - 2c - 3) / (c^2 - 4) - 1.