Question 37223
To eliminate the denominator you have to multiply all the expression by (x-1)(x-2)(2). 

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

Reducing common factors we get:

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


Now we have to expand and reduce.


2x-4-2x+2=x^2-2x-x+2 Expanding

0=x^2-2x-x+2x-2x+4-2 Reducing
0=x^2-3x+2     Final equation

Know we have to solve this problem, you can use the general formula.
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

You will get as solutions x=1,x=2