Answer
The solutions are $x=-1$ and $x=\dfrac{2}{3}$
Work Step by Step
$\dfrac{3x^{2}}{x-1}+2=\dfrac{x}{x-1}$
Multiply the whole equation by $x-1$:
$(x-1)\Big(\dfrac{3x^{2}}{x-1}+2=\dfrac{x}{x-1}\Big)$
$3x^{2}+2(x-1)=x$
Evaluate the indicated operations:
$3x^{2}+2x-2=x$
Take $x$ to the left side and simplify:
$3x^{2}+2x-x-2=0$
$3x^{2}+x-2=0$
Solve by factoring:
$(x+1)(3x-2)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x+1=0$
$x=-1$
$3x-2=0$
$3x=2$
$x=\dfrac{2}{3}$
The solutions are $x=-1$ and $x=\dfrac{2}{3}$
