Posted by Jamie on Monday, October 29, 2012 at 10:37pm.
simplify fractions first:
(x+3)/(x-6) - 2(x-6)/(x+3) + 8
now put all over common denominator of (x-6)(x+3)
(x+3)(x+3) - 2(x-6)(x-6) + 8(x+3)(x-6)
---------------------------------------
(x-6)(x+3)
= (7x^2+6x-207)//(x^2-3x-18)
The above answer is not really a satisfying "simplification." How about this?
x+3/x-6 = 1 + 9/(x-6)
x-6/x+3 = 1 - 9/(x+3)
so, we have
1 + 9/(x-6) + 2(1 - 9/(x+3)) + 8
9/(x-6) - 18/(x+3) + 11
"-" got lost.
Of course, I meant
9/(x-6) + 18/(x+3) + 7
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