Question 92045
1- 2x-1/x^2-4 over (or divided by) 1+ 1/x-2 
[1 -(2x-1)/(x^2-4)] / [1 + 1/(x-2)]

[[(x^2-4)-(2x-1)]/(x^2-4)] / [x-2+1]/(x-2)

= [[x^2-2x-3]/(x^2-4)] / [(x-1)/(x-2)]
Invert the denominator and multiply as follows:

= [(x-3)(x+1)/(x-2)(x+2)] * [(x-2)/(x-1)]
Cancel where you can to get:

= [(x-3)(x+1)]/[(x+2)(x-1)]

Cheers,
Stan H.