Question 1023119
{{{(2x-4)/(x^2+x-2) = (2x-4)/((x-1)(x+2))}}}

==> Domain of s(x) is ({{{-infinity}}}, -2)u(-2,1)u(1,{{{infinity}}}).

To find the range of s(x), let {{{y = (2x-4)/(x^2+x-2)}}}

==> {{{yx^2+yx-2y = 2x-4}}}
==> {{{yx^2+(y-2)x+(4-2y) = 0}}}, a quadratic equation in x with coefficients in terms of y.  For such expression to have real roots, the discriminant 

{{{b^2 - 4ac = (y-2)^2 - 4y(4-2y) >=0}}}

<==> {{{(y-2)^2 +8y(y-2) >=0}}}
<==> {{{(y-2)(9y-2) >=0}}}.
The solution to this inequality is the union ({{{-infinity}}}, 2/9]u[2, {{{infinity}}}) .

Incidentally this is also the range of s(x).