[(a^2-16b^2)/(2a-8b)] divided by [4a+16b)/(8a+24b)]
can be written as:
The division sign can be changed to a multiplication if we invert the denominator to get:
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?
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