Expert: Scott A Wilson - 3/31/2011

Question
Perform the indicated operations and simplify the results, leave your answer in factor form.
6-3x/x^2-4  -  12/2x+4

The result should be -9/x+2
I cant figure out how to work it out with the dominators.

Thank you in advance!

Answer
Note that x^2-4 = (x+2)(x-2) and that 2x+4 = 2(x+2).
Thus, multiply the 1st by 2/2 and the 2nd by (x-2)/(x-2) to get the same denominator,
which would then be 2(x-2)(x+2) = 2(x^2-4).

That gives 2(6-3x)/[2(x^2-4)] - 12(x-2)/[2(x^2-4)].
Combining fractions gives [2(6-3x) - 12(x-2)]/[2(x^2-4)].
That works out to (12 - 6x - 12x + 24)/[2(x^2-4)].
That combines to (36-18x)/[2(x^2-4)].
Dividing the top and bottom by 2 gives (18-9x)/(x^2-4).

This doesn't look right, but if we factor we get 9(2-x)/[(x-2)(x+2)]
and can see that (2-x)/(x-2) = -1, so we have -9/(x+2).