Question

divide.\\(\frac{3v^{5}+9v^{3}}{-v^{2}}\\)\\(\\)simplify your answer as much as possible.

Explanation:

Step1: Split the fraction

$\frac{3v^5 + 9v^3}{-v^2} = \frac{3v^5}{-v^2} + \frac{9v^3}{-v^2}$

Step2: Simplify each term

For $\frac{3v^5}{-v^2}$: use exponent rule $\frac{v^a}{v^b}=v^{a-b}$, so $\frac{3v^5}{-v^2} = -3v^{5-2} = -3v^3$
For $\frac{9v^3}{-v^2}$: $\frac{9v^3}{-v^2} = -9v^{3-2} = -9v$

Step3: Combine simplified terms

$-3v^3 -9v$

Answer:

$-3v^3 - 9v$