## College Algebra 7th Edition

$\displaystyle \frac{x}{2x-4}-2=\frac{1}{x-2}$ 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.