First, you must get each fraction over a common denominator which is #x^2 - 5x + 6#:
#(x - 2)/(x - 2) (x - 2)/(x - 3) + (x - 3)/(x - 3) (x - 3)/(x - 2) = (2x^2)/(x^2 - 5x + 6)#
#(x^2 - 4x + 4)/(x^2 - 5x + 6) + (x^2 - 6x + 9)/(x^2 - 5x + 6) = (2x^2)/(x^2 - 5x + 6)#
Next, add the fractions on the left side of the equation:
#((x^2 - 4x + 4) + (x^2 - 6x + 9))/(x^2 - 5x + 6) = (2x^2)/(x^2 - 5x + 6)#
#(2x^2 - 10x + 13)/(x^2 - 5x + 6) = (2x^2)/(x^2 - 5x + 6)#
We can now multiply each side of the equation by #x^2 - 5x + 6# to eliminate the fraction:
#(x^2 - 5x + 6) (2x^2 - 10x + 13)/(x^2 - 5x + 6) = (x^2 - 5x + 6) (2x^2)/(x^2 - 5x + 6)#
#cancel((x^2 - 5x + 6)) (2x^2 - 10x + 13)/cancel((x^2 - 5x + 6)) = cancel((x^2 - 5x + 6)) (2x^2)/cancel((x^2 - 5x + 6))#
#2x^2 - 10x + 13 = 2x^2#
We can now solve for #x#:
#2x^2 - 10x + 13 - 2x^2= 2x^2 - 2x^2#
#-10x + 13 = 0#
#-10x + 13 - 13 = 0 - 13#
#-10x = -13#
#(-10x)/-10 = (-13)/(-10)#
#x = 13/10#
