Divide. \[ \frac{-9 x^{4} u^{5}-21 x^{5} u+14 x^{5} u^{3}}{-3 x^{3} u^{2}} \]

To divide the expression \( \frac{-9 x^{4} u^{5}-21 x^{5} u+14 x^{5} u^{3}}{-3 x^{3} u^{2}} \), we can simplify it as follows: First, we can factor out a \(-3\) from the denominator: \[ \frac{-9 x^{4} u^{5} - 21 x^{5} u + 14 x^{5} u^{3}}{-3 x^{3} u^{2}} = \frac{1}{-3} \left( -9 x^{4} u^{5} - 21 x^{5} u + 14 x^{5} u^{3} \right) \cdot \frac{1}{x^{3} u^{2}} \] Now, we can distribute the division across each term in the numerator: 1. For the term \(-9 x^{4} u^{5}\): \[ \frac{-9 x^{4} u^{5}}{-3 x^{3} u^{2}} = 3 x^{4-3} u^{5-2} = 3 x u^{3} \] 2. For the term \(-21 x^{5} u\): \[ \frac{-21 x^{5} u}{-3 x^{3} u^{2}} = 7 x^{5-3} u^{1-2} = 7 x^{2} u^{-1} = \frac{7 x^{2}}{u} \] 3. For the term \(14 x^{5} u^{3}\): \[ \frac{14 x^{5} u^{3}}{-3 x^{3} u^{2}} = -\frac{14}{3} x^{5-3} u^{3-2} = -\frac{14}{3} x^{2} u \] Now, we can combine all these results: \[ 3 x u^{3} + \frac{7 x^{2}}{u} - \frac{14}{3} x^{2} u \] So, the final answer is: \[ 3 x u^{3} + \frac{7 x^{2}}{u} - \frac{14}{3} x^{2} u \]