![\begin{equation*} x^2-2x+3-(8)/(3x+2) \end{equation*}](https://img.qammunity.org/2023/formulas/mathematics/college/g6l7ctltkzjhphfq5d0htgsiqa4m7vok01.png)
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:
![(3x^3-4x^2+5x-2)/(3x+2)=\quad x^2-2x+3-(8)/(3x+2)](https://img.qammunity.org/2023/formulas/mathematics/college/19b7vnxnrvqmhti8fiu57clnni1atcvmhj.png)
Note that the remainder is written above the divisor on the final answer.