Exponents and Polynomials
Dividing a polynomial by a monomial: Multivariate

Divide.
\[
\left(21 u^{2} z^{4}-13 u^{3} z^{5}+15 u^{6} z^{6}\right) \div\left(-3 u^{3} z^{5}\right)
\]

Simplify your answer as much as possible.

Answer

Expert–verified

Hide Steps

Answer

\[\boxed{-7 u^{-1} z^{-1} + \frac{13}{3} - 5 u^{3} z}\]

Steps

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 ：\[\boxed{-7 u^{-1} z^{-1} + \frac{13}{3} - 5 u^{3} z}\]