Divide. Assume that no denominator equals zero. \( \begin{array}{ll}\left(3 m^{5}+m^{6}-m^{8}\right)+m^{3} & \text { c. } 3 m^{-2}+m^{-3}-m^{-5} \\ \text { a. } 3 m^{15}+m^{6}-m^{8} & \text { d. } 3 m^{2}+m^{3}-m^{5} \\ \text { b. } 3 m^{8}+m^{9}-m^{11} & \end{array} \)

To divide the expressions \((3 m^{5}+m^{6}-m^{8}+m^{3})\) by the expression \((3 m^{-2}+m^{-3}-m^{-5})\), we will first rearrange and simplify the numerator and denominator. **Step 1: Simplify the numerator.** Combine like terms in the numerator: - \(3m^5 + m^3 + m^6 - m^8 = m^6 - m^8 + 3m^5 + m^3\). - Rearranging gives \(m^6 - m^8 + 3m^5 + m^3 = m^3(1 + 3m^2 + m^3 - m^5)\). **Step 2: Simplify the denominator.** The denominator is \(3m^{-2} + m^{-3} - m^{-5}\). We can express it as: - \(3m^{-2} + m^{-3} - m^{-5} = m^{-5}(3m^3 + m^2 - 1)\). **Step 3: Division of the expressions.** Now, we divide: \[ \frac{m^3(1 + 3m^2 + m^3 - m^5)}{m^{-5}(3m^3 + m^2 - 1)} = m^{3 - (-5)} \cdot \frac{1 + 3m^2 + m^3 - m^5}{3m^3 + m^2 - 1} = m^{8} \cdot \frac{1 + 3m^2 + m^3 - m^5}{3m^3 + m^2 - 1}. \] The final expression is: \[ m^8 \frac{1 + 3m^2 + m^3 - m^5}{3m^3 + m^2 - 1}. \] This is your final result!