Answer
$$\frac{14x^3-12x+3}{2}$$
Work Step by Step
In order to divide monomials, we look for common terms in the numerator and the denominator that can be canceled out. Doing this, we find:
$$\frac{42x^5-36x^3+9x^2}{6x^2} \\ \frac{3x^2\left(14x^3-12x+3\right)}{6x^2}
\\ \frac{14x^3-12x+3}{2}$$
Note, if we wanted to check this answer, we could multiply the answer by the value we canceled out to see if that matched the original numerator.