## Precalculus (6th Edition)

$\dfrac{x}{x-3}=\dfrac{3}{x-3}+3$ Multiply the whole equation by $x-3$: $(x-3)\Big(\dfrac{x}{x-3}=\dfrac{3}{x-3}+3\Big)$ $x=3+3(x-3)$ Evaluate the indicated operations: $x=3+3x-9$ Take $3x$ to the left side: $x-3x=3-9$ Simplify both sides: $-2x=-6$ Solve for $x$: $x=\dfrac{-6}{-2}$ $x=3$ The original equation is undefined for $x=3$, so the equation has no solution.