Question 1130209: Solve the equation and show the check of your solution(s). If an answer is an excluded value, please state that on your paper.
x/x-2+8/x^2-8x+12=2x/x-6
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! (x/(x-2))+8/(x-2)(x-6), factoring the denominator, =2x/(x-6)
Multiply everything by (x-2)(x-6)
x(x-6)+8=2x(x-2)
x^2-6x+8=2x^2-4x
0=x^2+2x-8
0=(x+4)(x-2)
x=-4, 2
2 is extraneous, for the first term would be undefined
x=-4
check
-4/-6 first term is 2/3
8/(-6*-10), second term is 8/60
their sum is 48/60 or 4/5
equals -8/-10 which is 4/5
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