To determine if (n+4) is divisible by (n-1), we need to check if the remainder when (n+4) is divided by (n-1) is equal to 0.

Using the division algorithm, we can write (n+4) as (n-1) multiplied by some quotient plus the remainder:

n+4 = (n-1)q + r

where q is the quotient and r is the remainder.

If (n+4) is divisible by (n-1), then the remainder (r) must be equal to 0. Therefore, we have:

n+4 = (n-1)q + 0

Simplifying this equation, we get:

n+4 = (n-1)q

Expanding the right side, we have:

n+4 = nq - q

Rearranging the terms, we get:

4 + q = nq - n

Combining like terms, we have:

4 + q = (n-1)q

Subtracting q from both sides, we get:

4 = (n-1)q - q

Simplifying further, we have:

4 = (n-2)q

Since 4 is a constant, for (n+4) to be divisible by (n-1), the quotient (q) must be equal to 4/(n-2).

Therefore, (n+4) is divisible by (n-1) if and only if q = 4/(n-2).