SOLUTION: {{{(12-4a)/(2a^2-18)}}} I can't seem to figure this I came up with -2/a-6 I don't think that is right

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: {{{(12-4a)/(2a^2-18)}}} I can't seem to figure this I came up with -2/a-6 I don't think that is right       Log On


   

Question 128521: %2812-4a%29%2F%282a%5E2-18%29
I can't seem to figure this
I came up with -2/a-6 I don't think that is right
Answer by marcsam823(57) About Me  (Show Source):
You can put this solution on YOUR website!

1. Factor a -4 out of the numerator:
%2812+-+4a%29=+-4%28-3+%2B+a%29+=+-4%28a+-+3%29
2. Factor a 2 out of the denominator:
%282a%5E2+-+18%29+=+2%28a%5E2+-+9%29
3. a%5E2+-+9 is the difference of two perfect squares so we can use the formula: %28x%5E2+-+y%5E2%29+=+%28x+-+y%29%2A%28x+%2B+y%29
Therefore:
%28a%5E2+-+9%29+=+%28a+-+3%29%2A+%28a+%2B+3%29
4. Our expression is now:
-4%28a+-+3%29%2F%28%282%29%2A%28a+-+3%29%2A%28a+%2B+3%29%29
5. Simplify by
a) cancelling out the (a - 3) term
b) dividing 2 out of both numerator and denominator
6. We are left with:
-2%2F%28a+%2B+3%29
You were close!