[tex]\begin{equation*} x^2-2x+3-\frac{8}{3x+2} \end{equation*}[/tex]
1) Since the degree of the denominator is lower than the numerator's we can divide these expressions through long division that way:
As we can see in each step the aim is to cancel the leading coefficient.
2) Note that a Long Division, has a way to write its answer so we can tell that this is the answer:
[tex]\frac{3x^3-4x^2+5x-2}{3x+2}=\quad x^2-2x+3-\frac{8}{3x+2}[/tex]
Note that the remainder is written above the divisor on the final answer.
