# Math

posted by .

How do you simplify this?

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

• Math -

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 -

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 -

"-" got lost.
Of course, I meant

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

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