Answer
$2x^2 +x+5+\frac{6}{x-2}$.
Work Step by Step
The given expression is
$(2x^3-3x^2+3x-4)\div(x-2)$
$\begin{matrix}
& 2x^2 & +x &+5 & & \leftarrow &Quotient\\
&-- &-- &--&--& \\
x-2) &2x^3&-3x^2&+3x&-4 & \\
& 2x^3 & -4x^2 & & & \leftarrow &2x^2(x-2) \\
& -- & -- & & & \leftarrow &subtract \\
& 0 & x^2 & +3x & & \\
& & x^2 & -2x & & \leftarrow & x(x-2) \\
& & -- & -- & & \leftarrow & subtract \\
& & 0&5x &-4 & \\
& & & 5x& -10 & \leftarrow & 5(x-2) \\
& & & -- & -- & \leftarrow & subtract \\
& & & 0 & 6 & \leftarrow & Remainder
\end{matrix}$
The answer is
$\Rightarrow Quotient + \frac{Remainder}{Divisor}$
$\Rightarrow 2x^2 +x+5+\frac{6}{x-2}$.
