Step 1 :\[\frac{21 u^{2} z^{4}}{-3 u^{3} z^{5}} - \frac{13 u^{3} z^{5}}{-3 u^{3} z^{5}} + \frac{15 u^{6} z^{6}}{-3 u^{3} z^{5}}\]
Step 2 :Simplify each term:
Step 3 :\[= -7 u^{-1} z^{-1} + \frac{13}{3} - 5 u^{3} z\]
Step 4 :So, the simplified form of the given expression is:
Step 5 :\[\boxed{-7 u^{-1} z^{-1} + \frac{13}{3} - 5 u^{3} z}\]