Answer
$4h-7$
Work Step by Step
Given
\begin{equation}
\left(4 h^3-7 h^2-12 h+21\right) \div\left(h^2-3\right)
\end{equation} Use long division.
$$
\begin{array}{r}
4h-7\phantom{)} \\
h^2-3{\overline{\smash{\big)}\,4 h^3-7 h^2-12 h+21\phantom{)}}}\\
\underline{-~\phantom{(}(4h^3-12h)\phantom{-b)}}\\
0-7h^2+21\phantom{)}\\
\underline{-~\phantom{()}(-7h^2+21)}\\
0\phantom{)}
\end{array}
$$ The solution is
\begin{equation}
\frac{4 h^3-7 h^2-12 h+21}{h^2-3}=4h-7
\end{equation}
