Posted by **Sarah** on Sunday, December 27, 2009 at 5:28pm.

Simplify:

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

Please Help!!!! Thanks.

- Math -
**MathMate**, Sunday, December 27, 2009 at 6:10pm
[(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?

- Math -
**Sarah**, Sunday, December 27, 2009 at 6:40pm
Yes. thanks.

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