SOLUTION: Add the fractions and simplify. {{{(9/(w + 6)) - ((w^2-2w)/ (w^2 + 4w - 12))}}}

Algebra ->  Rational-functions -> SOLUTION: Add the fractions and simplify. {{{(9/(w + 6)) - ((w^2-2w)/ (w^2 + 4w - 12))}}}       Log On


   

Question 879618: Add the fractions and simplify.
%289%2F%28w+%2B+6%29%29+-+%28%28w%5E2-2w%29%2F+%28w%5E2+%2B+4w+-+12%29%29
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The quadratic denominator is (w-2)(w+6). Raise the first rational expression to higher terms using %28w-2%29%2F%28w-2%29=1.

%289%28w-2%29-%28w%5E2-2w%29%29%2F%28w%5E2%2B4w-12%29
%289w-18-w%5E2%2B2w%29%2F%28w%5E2%2B4w-12%29
%28-w%5E2%2B11w-18%29%2F%28w%5E2%2B4w-12%29
%28-1%29%28w%5E2-11w%2B18%29%2F%28w%5E2%2B4w-12%29
FACTORABLE NUMERATOR, and remember the factorization of the denominator:
%28-1%29%28w-2%29%28w-9%29%2F%28%28w-2%29%28w%2B6%29%29
%28-1%29cross%28%28w-2%29%29%28w-9%29%2F%28cross%28%28w-2%29%29%28w%2B6%29%29