Question 1041377
The domain of the expression is the set of all real numbers.  (The discriminant {{{b^2-4ac = -17}}} of the denominator implies that it itself  is never zero.)

Let {{{y = (x^2-3x+1)/(2x^2-3x+2)}}}.

==> {{{y(2x^2-3x+2) = x^2-3x+1}}} (after multiplication; note that the denominator is never zero)

==> {{{2yx^2-3yx+2y = x^2-3x+1}}} <==> {{{(2y-1)x^2+(3-3y)x+(2y-1) = 0}}}.

For x to have real values, the discriminant of this equation (with x as variable) must be greater than or equal to 0. 

==> {{{(3-3y)^2-4(2y-1)^2 >= 0}}} <==> {{{-7y^2-2y+5 >=0}}}, or

{{{7y^2+2y-5 <=0}}},

<==> {{{(7y-5)(y+1) <= 0}}}

The inequality is only true when y &#8712; [-1, 5/7].