Answer:
Step-by-step explanation:
[tex]\frac{2x}{x-1} -\frac{2x-5}{x^2-3x+2} =\frac{-3}{x-2} \\\frac{2x}{x-1} +\frac{3}{x-2} =\frac{2x-5}{x^2-3x+2} \\\frac{2x(x-2)+3(x-1)}{(x-1)(x-2)} =\frac{2x-5}{x^2-3x+2} \\\frac{2x^2-4x+3x-3}{x^2-2x-x+2} =\frac{2x-5}{x^2-3x+2} \\\frac{2x^2-x-3}{x^2-3x+2} =\frac{2x-5}{x^2-3x+2} \\x\neq 1,x\neq 2,x^2-3x+2\neq 0\\multiply~by~x^2-3x+2\\2x^2-x-3=2x-5\\2x^2-3x+2=0\\x=\frac{3\pm\sqrt{9-4*2*2} }{2*2} \\x=\frac{3 \pm\sqrt{-7} }{4} \\x=\frac{3 \pm \sqrt{7} i}{4}[/tex]
