#### Answer

$3a^{2}-3a+1+\frac{2}{3a+2}$

#### Work Step by Step

To divide polynomials using long division, the numerator (what is being divided) goes inside the division sign and the denominator (what the term inside is being divided by) goes outside the division sign. To solve by long division, think about what must be multiplied to the first term of the outside polynomial to equal the first term of the inside polynomial. Multiply and subtract the new polynomial from the inside polynomial, then bring down the next term. Continue this process until all terms have been brought down. Whatever is being multiplied to the term goes above the division symbol. The resulting term on top of the division symbol will be the answer, assuming the remainder is zero. If the remainder is not zero, then the final answer is the term on top of the division symbol, plus the remainder over the original term outside the division symbol. See attached image for worked out solution.