solve and check equation

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1      -          2            = 1

x-2       x^2-2x

Jun 25th, 2015

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   -      = 1

x-2     x^2-2x


(1/x-2)-(2/x(x-2)  =1

therefore,

x/x(x-2) -   2/x(x-2) =1           (making common denominator)

x-2/x(x-2) =1

1/x =1            (cancelling (x-2) )

x=1   

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 25th, 2015

I get the LCM as X(X-2).  If I apply LCM to right side of equation to each term to cancel out the fraction, I get 

x(x-2) (1/x-2) - 2/x(x-2) . x(x-2) = 1

cancelling x(x-2)  x-2=1 x=3.  Also, could I have made this quadratic equation set to zero and solved for X, in which case x=2 or x=1.   

I am a bit confused on the LCM.  I get x(x-2) and you appear to get just (x-2), please explain.  Also could solving and setting equation to zero also have worked???

Jun 25th, 2015

u should make the denominator common.

here x(x-2) is the common denominator.

so multiply numerator and denominator of 1/x-2   by x.

and follow as given in answer.

Jun 25th, 2015

I see my error.  Thanks!!!

Jun 25th, 2015

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