Solve the Extraneous Solutions ?

You're worst enemy (aside from arithmetic mistakes), while you're trying to solve a rational equation, is forgetting to check for extraneous solutions (things that look like solutions but aren't). The moment you find yourself multiplying both sides of an equation by anything involving variable, extraneous solutions become a possibility.

Your defense will be good bookkeeping. This does not come automatically. It takes practice, Here's what you need to do. As you do your exercises, watch for the step when you clear denominators. At that point, write a little note to yourself that there might be extraneous solutions. And keep writing it down on each line, until you're done.

Here's another worked-out example, together with the kind of notes you should write:

Although 7 is indeed a solution to the original equation, 2 is not. The only solution is 7.

(So why don't you see your teacher making notes like this? Because math teachers have enough experience to keep the information in their heads. If you're good enough to "take notes" like this in your head, that's great. If not... well, you know what to do!)