Answer
$\frac{6x^3+4 x-15}{x-1}=6x^2+6x+10-\frac{5}{x-1}$
Work Step by Step
Given \begin{equation}
\begin{aligned}
\left(6 x^3+4 x-15\right) \div(x-1)
\end{aligned}
\end{equation} Use synthetic division. \begin{equation}
\begin{array}{r|rrrr}
1&6 & 0 & 4 &-15 \\
& & 6 & 6& 10 \\
\hline &6 & 6 & 10 & -5
\end{array}
\end{equation} The solution is \begin{equation}
\begin{aligned}
\frac{6x^3+4 x-15}{x-1}=6x^2+6x+10-\frac{5}{x-1}.
\end{aligned}
\end{equation}
