Answer:
Step-by-step explanation:
To simplify the expression (6a^2 - 3a + 9)/(3a - 2), we can use polynomial long division. Here is the step-by-step process:
1. First, set up the division in the same way you would for numerical division, placing 6a^2 - 3a + 9 inside the division bracket and 3a - 2 outside.
2. Divide the first term of the numerator by the first term of the denominator. 6a^2 divided by 3a is 2a. Write this above the division bracket.
3. Multiply the entire denominator by 2a and write the result below the numerator, aligning similar terms:
2a
___________
3a - 2 | 6a^2 - 3a + 9
6a^2 - 4a
___________
a + 9
4. Subtract the result from the numerator:
(6a^2 - 3a + 9) - (6a^2 - 4a) = a + 9
5. Since a cannot be divided by 3a - 2, the result is (a + 9)/(3a - 2).
Therefore, the simplified expression is (2a + 1) + (9/(3a - 2)).