Divide. Write your answer in simplest form. \[ \frac{4 k-8}{7 k} \div(2 k+1) \]

To solve the division of the expression \(\frac{4k-8}{7k} \div (2k+1)\), we first recall that dividing by a fraction is equivalent to multiplying by its reciprocal. 1. Rewrite the division as multiplication: \[ \frac{4k-8}{7k} \times \frac{1}{2k+1} \] 2. Next, simplify the expression. We can factor the numerator \(4k - 8\): \[ 4k - 8 = 4(k - 2) \] 3. Substitute the factored form back into the expression: \[ \frac{4(k - 2)}{7k} \times \frac{1}{2k + 1} \] 4. Now, write this as a single fraction: \[ \frac{4(k - 2)}{7k(2k + 1)} \] 5. The fraction \(\frac{4(k - 2)}{7k(2k + 1)}\) is already in its simplest form because there are no common factors to cancel out. Thus, the final answer is: \[ \frac{4(k - 2)}{7k(2k + 1)} \]