Answer
$x+5$
Work Step by Step
$\begin{array}{ccccccccccc}
& &x & +5 & & \\
& &--&--&--&\\
x-2&) &x^{2} &+3x& -10 & \\
& &x^{2} & -2x& & \color{red}{\leftarrow \small{x(x-2) } } \\
& &--&-- & & \color{red}{ \small{subtract}} \\
& & & 5x & -10 & \\
& & & 5x & -10 & \color{red}{\leftarrow \small{5(x-2) } }\\
& & &--&-- & \color{red}{ \small{subtract}} \\
& & & & 0 &
\end{array}$
Quotient = $x+5$
Remainder = $0$.
$\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$
$\displaystyle \frac{x^{2} +3x -10}{x-2}$ = $x+5$
