Posted by **Jamie** on Monday, October 29, 2012 at 10:37pm.

How do you simplify this?

(x+3/x-6)-2/(x+3/x-6)+8

- Math -
**Steve**, Monday, October 29, 2012 at 10:55pm
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)

- Math -
**Steve**, Tuesday, October 30, 2012 at 10:25am
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

- Math -
**Steve**, Tuesday, October 30, 2012 at 10:26am
"-" got lost.

Of course, I meant

9/(x-6) + 18/(x+3) + 7

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