Posted by math on Thursday, January 13, 2011 at 8:47am.
did you notice that
x^2 - 7x + 12 = (x-4)(x-3) which happen to be denominators of the first 2 terms?
So the LCD is (x-4)(x-3)
Multiply each term by that LCD to get
2x(x-3) + 4(x-4) = 8
2x^2 + 4x - 30 = 0
x^2 + 2x - 15 = 0
(x+5)(x-3) = 0
x = -5 or x = 3
BUT x=3 would make the expression undefined,
so
x = -5
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