Chapter 7 - Rational Functions - 7.2 Simplifying Rational Expressions - 7.2 Exercises - Page 576: 54

$t+9$

Given \begin{equation} \begin{aligned} \left(t^2+7 t-18\right) \div(t-2) \end{aligned} \end{equation} Use synthetic division. \begin{equation} \begin{array}{r|rrr} 2& 1 & 7 & -18 \\ & & 2 & 18 \\ \hline & 1 & 9 & 0 \end{array} \end{equation} The solution is \begin{equation} \begin{aligned} \frac{t^2+7 t-18}{t-2}= t+9 \end{aligned} \end{equation}