To simplify this expression, we will first expand the second part of the expression (6a+1/a-3+ 6a-1/a+3) by multiplying it out.
(6a+1/a-3) + (6a-1/a+3= 6a + 1/a - 3 + 6a - 1/a + = 12a - 3 + = 12a
So the expression now becomes:
A^2 - 9 / 2a^2 + 1 * 12a
Now, we will distribute 12a to the terms in the numerator:
A^2 12a - 9 / 2a^2 12a + 1 * 12a
= 12a^3 - 108a / 24a^2 + 12a
= (12a(a^2 - 9)) / (24a^2 + 12a)
= (12a(a+3)(a-3) / 12a(2a+1))
= (a+3)(a-3) / 2(2a+1)
Therefore, the simplified expression is:
(a+3)(a-3) / 2(2a+1)
To simplify this expression, we will first expand the second part of the expression (6a+1/a-3+ 6a-1/a+3) by multiplying it out.
(6a+1/a-3) + (6a-1/a+3
= 6a + 1/a - 3 + 6a - 1/a +
= 12a - 3 +
= 12a
So the expression now becomes:
A^2 - 9 / 2a^2 + 1 * 12a
Now, we will distribute 12a to the terms in the numerator:
A^2 12a - 9 / 2a^2 12a + 1 * 12a
= 12a^3 - 108a / 24a^2 + 12a
= 12a^3 - 108a / 24a^2 + 12a
= (12a(a^2 - 9)) / (24a^2 + 12a)
= (12a(a+3)(a-3) / 12a(2a+1))
= (a+3)(a-3) / 2(2a+1)
Therefore, the simplified expression is:
(a+3)(a-3) / 2(2a+1)