Answer:
[tex]x=\frac{3}{4}+i\frac{\sqrt{7}}{4},\:x=\frac{3}{4}-i\frac{\sqrt{7}}{4}[/tex]
Step-by-step explanation:
simplify [tex]\frac{-3}{x-2}[/tex] by putting the negative sign on the outside. [tex]\frac{2x}{x-1}-\frac{2x-5}{x^2-3x+2}=-\frac{3}{x-2}[/tex]
find the LCM of the denominators. It is (x-1)(x-2). Multiply by the LCM:
[tex]\frac{2x}{x-1}\left(x-1\right)\left(x-2\right)-\frac{2x-5}{x^2-3x+2}\left(x-1\right)\left(x-2\right)=-\frac{3}{x-2}\left(x-1\right)\left(x-2\right)[/tex]
Simplify:
[tex]2x\left(x-2\right)-\left(2x-5\right)=-3\left(x-1\right)[/tex]
solve: [tex]x=\frac{3}{4}+i\frac{\sqrt{7}}{4},\:x=\frac{3}{4}-i\frac{\sqrt{7}}{4}[/tex]
