Multiply both sides by $x$.

$\frac{6}{x}=x-1$

$x\cdot\frac{6}{x}=(x-1)\cdot x$

$6=x^2-x$

Move all terms to one side.

$0=x^2−x−6$

Factor.

$0=(x+2)(x−3)$

Use the Zero Product Property.

$x=−2$ or $x=3$

There are two solutions to this equation. One of them is $−3$.