Simplify:

[(a^2-16b^2)/(2a-8b)] divided by [4a+16b)/(8a+24b)]

Please Help!!!! Thanks.

[(a^2-16b^2)/(2a-8b)] divided by [4a+16b)/(8a+24b)]

can be written as:
[(a^2-16b^2)/(2a-8b)]/[4a+16b)/(8a+24b)]
The division sign can be changed to a multiplication if we invert the denominator to get:
[(a^2-16b^2)/(2a-8b)]*[(8a+24b)/4a+16b)]
which readily simplifies to two terms in the numerator and two terms in the denominator:
[(a^2-16b^2)*(8a+24b)] / [(2a-8b)*(4a+16b)]

Factorize terms in the numerator:
(a^2-16b^2) = (a+4b)(a-4b)
(8a+24b) = 8(a+3b)

Factorize terms in the denominator:
(2a-8b) = 2(a-4b)
(4a+16b) = 4(a+4b)

Since most terms cancel out in the numberator and denominator, you are left with a binomial in the numerator.

Can you take it from here?

Yes. thanks.

To simplify the given expression, we need to divide the numerator by the denominator.

Step 1: Factorize the numerator and denominator
In the numerator, we have the difference of squares, a^2 - 16b^2, which can be factored as (a - 4b)(a + 4b).
In the denominator, we can factor out a common factor of 4 from both terms, resulting in 4(a + 4b) / 4(2a + 6b).

Step 2: Simplify the expression
Now that we have factored the numerator and denominator, we can cancel out any common factors. In this case, we can cancel out the factor of 4 in the numerator and denominator:
((a - 4b)(a + 4b))/(2a + 6b)

Step 3: Simplify further if possible
If there are any common factors remaining in the numerator and denominator, we can cancel them out. However, in this case, there are no common factors to cancel.

Thus, the simplified expression is:
(a - 4b)(a + 4b) / (2a + 6b)

And that is the simplified form of the given expression.