SOLUTION: Simplify the following expressions. (a) {{{ (m(1/(m^2-4)))/(1/(m+2)) }}} (b) {{{ ((ac+ad+bc+bd)/(a^2-b^2))((a^3-b^3)/(2a^2+2ab+2b^2)) }}}

Algebra ->  Radicals -> SOLUTION: Simplify the following expressions. (a) {{{ (m(1/(m^2-4)))/(1/(m+2)) }}} (b) {{{ ((ac+ad+bc+bd)/(a^2-b^2))((a^3-b^3)/(2a^2+2ab+2b^2)) }}}      Log On


   

Question 718129: Simplify the following expressions.
(a) +%28m%281%2F%28m%5E2-4%29%29%29%2F%281%2F%28m%2B2%29%29+
(b)
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
In (a) you invert and multiply to get
(1) m%281%2F%28m%5E2-4%29%29%2A%28m%2B2%29
Now factor
(2) %28m%5E2-4%29+=+%28m%2B2%29%2A%28m-2%29 and put into (1) and get
(3) (a) m%2F%28m-2%29
For (b) we need to factor all four polynomials.
First one
(4) %28ac+%2Bad+%2Bbc+%2Bbd%29+=+a%28c%2Bd%29+%2Bb%28c%2Bd%29 or
(5) %28ac+%2Bad+%2Bbc+%2Bbd%29+=+%28a%2Bb%29%2A%28c%2Bd%29
Second one
(6) a%5E2-b%5E2+=+%28a%2Bb%29%2A%28a-b%29
Third one
(7) %28a%5E3-b%5E3%29+=+%28a-b%29%2A%28a%5E2%2Bab%2Bb%5E2%29
Fourth one
(8) %282a%5E2%2B2ab%2B2b%5E2%29+=+2%2A%28a%5E2%2Bab%2Bb%5E2%29
Replacing each polynomial of b) with its factored form and cancelling like factors yields
(9) (b) %28c%2Bd%29%2F2