One True, One False

Solve $\frac{{x}^{2}}{x+3} = \frac{9}{x+3}$. Multiply both sides by $x+3$: ${x}^{2} = 9$. Take the square root of both sides, and there are two candidates: x = 3 or x = -3.

Check each one in the original. At 3, the bottom is 6, and both sides are 9/6: it stands. At -3, the bottom is 0: it is extraneous and goes. The solution is x = 3 only. One false answer does not spoil the others, because it comes from one particular value making a bottom 0.

So check every candidate on its own, and throw out only the ones that make a bottom 0.