a^3 - 8b^3/6b^2 - ba- a^2 /
3a^3b + 6a^2b^2 + 12ab^3/ a^2 - 9b^2
perform indicated operation and reduce to lowest terms
To perform the indicated operation and reduce the expression to its lowest terms, we need to simplify each individual fraction and then combine them.
First, let's simplify the first fraction: (a^3 - 8b^3) / (6b^2 - ba - a^2)
To factor the numerator, we can use the formula for the difference of cubes: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Using this formula, we can rewrite the numerator as (a - 2b)(a^2 + 2ab + 4b^2).
The denominator doesn't factor easily, so let's write it as (-a^2 + ba - 6b^2) to simplify further.
Now, the fraction becomes [(a - 2b)(a^2 + 2ab + 4b^2)] / [-a^2 + ba - 6b^2].
Next, let's simplify the second fraction: (3a^3b + 6a^2b^2 + 12ab^3) / (a^2 - 9b^2)
We can factor out the common factor of 3ab from each term in the numerator:
3ab(a^2 + 2ab + 4b^2) / (a^2 - 9b^2).
Now, we have the following fractions:
[(a - 2b)(a^2 + 2ab + 4b^2)] / (-a^2 + ba - 6b^2) and 3ab(a^2 + 2ab + 4b^2) / (a^2 - 9b^2).
To combine the fractions, we need to find the least common denominator (LCD) of (-a^2 + ba - 6b^2) and (a^2 - 9b^2), which is (a^2 - 9b^2).
Now, we can rewrite the fractions with the common denominator:
[(a - 2b)(a^2 + 2ab + 4b^2)] * (a^2 - 9b^2) / ((-a^2 + ba - 6b^2) * (a^2 - 9b^2))
And,
3ab(a^2 + 2ab + 4b^2) * (-a^2 + ba - 6b^2) / ((a^2 - 9b^2) * (a^2 - 9b^2))
Finally, we can simplify the expression further if there are any common factors in the numerator and denominator, or if there are any terms that can be canceled out.
Please double-check the original question as there seems to be some ambiguity in the expression you provided.