To simplify this expression, let's first simplify the terms inside the parentheses:
(3a-1)/(3a+1) - (3a+1)/(3a-1)
To simplify these two fractions, we need to find a common denominator. The common denominator in this case is (3a+1)(3a-1).
(3a-1)/(3a+1) = [(3a-1)(3a-1)]/[(3a+1)(3a-1)] = (9a^2 -6a + 1)/(9a^2 - 1)
(3a+1)/(3a-1) = [(3a+1)(3a+1)]/[(3a-1)(3a+1)] = (9a^2 + 6a +1)/(9a^2 - 1)
Now, let's substitute these two fractions back into the original expression and simplify further:
[(9a^2 -6a + 1)/(9a^2 - 1)] - [(9a^2 + 6a +1)/(9a^2 - 1)]
= [9a^2 -6a + 1 - 9a^2 - 6a - 1]/(9a^2 - 1)
= [-12a]/(9a^2 - 1)
Now, we have:
[-12a]/(9a^2 - 1) * 4a/(21a + 7)
Expanding the expression further:
(-12a * 4a)/(9a^2 - 1)(21a + 7)
= (-48a^2)/(189a^3 + 63a - 21a - 7)
= (-48a^2)/(189a^3 + 42a - 7)
Therefore, the simplified form of the given expression is (-48a^2)/(189a^3 + 42a - 7).
To simplify this expression, let's first simplify the terms inside the parentheses:
(3a-1)/(3a+1) - (3a+1)/(3a-1)
To simplify these two fractions, we need to find a common denominator. The common denominator in this case is (3a+1)(3a-1).
(3a-1)/(3a+1) = [(3a-1)(3a-1)]/[(3a+1)(3a-1)] = (9a^2 -6a + 1)/(9a^2 - 1)
(3a+1)/(3a-1) = [(3a+1)(3a+1)]/[(3a-1)(3a+1)] = (9a^2 + 6a +1)/(9a^2 - 1)
Now, let's substitute these two fractions back into the original expression and simplify further:
[(9a^2 -6a + 1)/(9a^2 - 1)] - [(9a^2 + 6a +1)/(9a^2 - 1)]
= [9a^2 -6a + 1 - 9a^2 - 6a - 1]/(9a^2 - 1)
= [-12a]/(9a^2 - 1)
Now, we have:
[-12a]/(9a^2 - 1) * 4a/(21a + 7)
Expanding the expression further:
(-12a * 4a)/(9a^2 - 1)(21a + 7)
= (-48a^2)/(189a^3 + 63a - 21a - 7)
= (-48a^2)/(189a^3 + 42a - 7)
Therefore, the simplified form of the given expression is (-48a^2)/(189a^3 + 42a - 7).