(3a^2+6ab-a-2b)/(9a^2-6a+1)

OK - one more freebie. After this, show some work and we'll see how you're doing.

3a^2+6ab-a-2b = 3a^2-a + 6ab-2b
= a(3a-1) + 2b(3a-1) = (a-2b)(3a-1)

9a^2-6a+1 = (3a-1)(3a-1)

divide and you have (a-2b)/(3a-1)

The numerator, you have to factor by grouping.

Group: (3a^2 + 6ab) + (-a -2b)
Take out the common factor in each group and then you should see two identical factors. Write that factor down once and your second factor is what is left over (actually, what you factored out from each part.)

The denominator can be factored as a perfect square.

You should be able to cancel out like factors to reduce the fraction.

To simplify the expression (3a^2 + 6ab - a - 2b) / (9a^2 - 6a + 1), we can follow these steps:

Step 1: Factor both the numerator and the denominator, if possible.
The numerator (3a^2 + 6ab - a - 2b) cannot be factored further as it does not have any common factors.

The denominator (9a^2 - 6a + 1) can be factored using the quadratic formula or by inspection. However, in this case, it is not possible to factor it further.

Step 2: Check if there are any common factors between the numerator and denominator.
In this case, there are no common factors between the numerator and denominator.

Step 3: Simplify the expression by canceling out common factors.
Since there are no common factors, we cannot simplify the expression further.

Thus, the expression (3a^2 + 6ab - a - 2b) / (9a^2 - 6a + 1) cannot be simplified any further.