Question

This last one I need help on too

Answer 1

Answer:

$x=\frac{3}{4}+i\frac{\sqrt{7}}{4},\:x=\frac{3}{4}-i\frac{\sqrt{7}}{4}$

Step-by-step explanation:

simplify $\frac{-3}{x-2}$ by putting the negative sign on the outside. $\frac{2x}{x-1}-\frac{2x-5}{x^2-3x+2}=-\frac{3}{x-2}$

find the LCM of the denominators. It is (x-1)(x-2). Multiply by the LCM:

$\frac{2x}{x-1}\left(x-1\right)\left(x-2\right)-\frac{2x-5}{x^2-3x+2}\left(x-1\right)\left(x-2\right)=-\frac{3}{x-2}\left(x-1\right)\left(x-2\right)$

Simplify:

$2x\left(x-2\right)-\left(2x-5\right)=-3\left(x-1\right)$

solve: $x=\frac{3}{4}+i\frac{\sqrt{7}}{4},\:x=\frac{3}{4}-i\frac{\sqrt{7}}{4}$