Question 197763
please  check  original  problem
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1/x - 1/(x-1) = 6
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mult  thru  by  x(x-1)
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(x-1) - x =6x(x-1)
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x-1-x =6x^2 -6x
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0 = 6x^2 -6x +1
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cannot  factor  ,,therefore use  quadratic  equation
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let  a  =(6),,b=(-6),,,c=(1)
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x= { -(-6) +/- sqrt { (-6)^2 -4 (6)(1) }  } /2(6)
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x = { 6 +/- sqrt (36-24) } 12
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x= 1/2 +/- ( 3.464) / 12
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x= 1/2 +/- .2887
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x= .7886,,, or   .2113
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checking
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for  .2113,,,, 1/.2113 - 1/ (.2113 -1) = 4.73 +1.267 =6 ,,,ok
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for  .7886,,, 1/.7886 - 1/(.7886-1) = 1.268 + 4.730 = 6,,ok