SOLUTION: [(A^3-B^3)/(A^2-b^2)] / [(a^2+ab+b^2)/(a^2+2ab+b^2)]

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Question 793088: [(A^3-B^3)/(A^2-b^2)] / [(a^2+ab+b^2)/(a^2+2ab+b^2)]
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let
(1) a%5E3-b%5E3
(2) a%5E2-b%5E2
(3) a%5E2%2Bab%2Bb%5E2
(4) a%5E2%2B2%2Aab%2Bb%5E2
Then we have
(4) ((1)/(2))*((4)/(3))
The first expression (1) factors into
(5) %28a-b%29%2A%28a%5E2%2Bab%2Bb%5E2%29
and the second expression (2) factors into
(6) %28a-b%29%2A%28a%2Bb%29
Then (1)/(2) reduces to
(7) %28a-b%29%2A%28a%5E2%2Bab%2Bb%5E2%29%2F%28%28a-b%29%2A%28a%2Bb%29%29 or
(8) %28a%5E2%2Bab%2Bb%5E2%29%2F%28a%2Bb%29
The third expression (3) does not factor and the fourth expression (4) factors into
(9) %28a%2Bb%29%5E2 so that (4)/(3) is
(10) %28a%2Bb%29%5E2%2F%28a%5E2%2Bab%2Bb%5E2%29
Now carry out the operatios of (4) to get the answer
(11)
which reduces to
(12) a+b
Answer: a+b