Answer
No solution.
Work Step by Step
$\displaystyle \frac{x}{2x-4}-2=\frac{1}{x-2}$
We multiply both sides by $2(x-2)$:
$x-2*2(x-2)=2$
Then we distribute and simplify:
$x-4x+8=2$
$-3x=-6$
$x=2$
But we see that if we use $x=2$ in the original equation, we get division by 0, which is undefined. (This happened because we multiplied both sides by $x-2$, which is 0 when $x=2$.
Multiplying both sides of an equation by 0 changes it.) Therefore there is no solution.
