SOLUTION: I cannot get this answer right. my teacher has provided the answer and we have to do the figuring. I keep coming up with a different answer than provided; therefore, my figuring is

Question 197763: I cannot get this answer right. my teacher has provided the answer and we have to do the figuring. I keep coming up with a different answer than provided; therefore, my figuring is wrong. The problem is:
1/x-1/x-1=6.
The answer provided is{-2,3} How is this answer figured, I keep getting a fraction for an answer. Please help
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
please check original problem
.
1/x - 1/(x-1) = 6
.
mult thru by x(x-1)
.
(x-1) - x =6x(x-1)
.
x-1-x =6x^2 -6x
.
0 = 6x^2 -6x +1
.
cannot factor ,,therefore use quadratic equation
.
let a =(6),,b=(-6),,,c=(1)
.
x= { -(-6) +/- sqrt { (-6)^2 -4 (6)(1) } } /2(6)
.
x = { 6 +/- sqrt (36-24) } 12
.
x= 1/2 +/- ( 3.464) / 12
.
x= 1/2 +/- .2887
.
x= .7886,,, or .2113
.
checking
.
for .2113,,,, 1/.2113 - 1/ (.2113 -1) = 4.73 +1.267 =6 ,,,ok
.
for .7886,,, 1/.7886 - 1/(.7886-1) = 1.268 + 4.730 = 6,,ok
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