<PRE><B>Question 230719</B>
((1/(x-2))+1)/((1/(x-2))-1))
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= [1+ (x-2)]/(x-2) / [1-(x-2)]/(x-2)
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Invert the denominator and multiply:
= [1+ (x-2)]/(x-2) *(x-2)/ [1-(x-2)]
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Cancel the (x-2) factors:
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= [1+ (x-2)] * 1/ [1-(x-2)]

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= [x-1]/[3-x]
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Cheers,
Stan H.</PRE>