SOLUTION: Please help me find the solutions to (1/(x-3)^2)+(2/(x-3))-24=0 I came up with the solution set as {11/4,19/6). I don't think this is right. Please steer me in the right directi

Question 56599: Please help me find the solutions to (1/(x-3)^2)+(2/(x-3))-24=0
I came up with the solution set as {11/4,19/6). I don't think this is right.
Please steer me in the right direction.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(1/(x-3)^2)+(2/(x-3))-24=0
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Let 1/(x-3)=w.
Rewrite the equation as:
w^2+2w-24=0
(w+6)(w-4)=0
w=-6 or w=4
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Now, change back to x notation:
If w=-6, -6=1/(x-3), then x-3=-(1/6); x=3-1/6 or 17/6
If w=4, 4=1/(x-3), then x-3=1/4; x=3 1/4 or 13/4
Cheers,
Stan H.

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