Note, that you refer to the previous version of the prep guide. I'd like to let you know that there is a newer version on the website now.

As always we keep on improving, to deliver the best and most up-to-date experience.

Here is the answer to your question.

There are two different problems mentioned in your inquiry.

**Quote:**

Does this equation have a solution?

(*x*² – 4*x* + 4)/(*x* – 2) = 0

As it had been written in the prep guide, the numerator can be transformed into (

*x* – 2)². It equals 0 only if

*x* = 2. But the denominator would be 0, if

*x* = 2. Division by 0 is undefined, so the equation has NO solution.

The WRONG way to solve was also provided in the prep guide, so that a student could see the trap. Apparently, you thought of it as of the proper one.

**Quote:**

However, if you divide the binomial into (*x* + 2)(*x* – 2)/(*x* – 2) = 0, then wouldn't you cancel out the matching (*x* – 2)s in the numerator and denominator, leaving you with (*x* + 2) = 0...making the solution *x* = -2?

This equation is (

*x*² – 4)/(

*x* – 2) = 0. Note, that it differs from the previous one.

The numerator, (

*x* + 2)(

*x* – 2), equals 0 when

*x* = -2 or

*x* = 2. However

*x* = 2 does not fit in the original equation, since the denominator must NOT equal 0. So

*x* = -2 is the only solution.

Note, that you can cancel out same expression, assuming it does not equal 0, but keep in mind the "prohibited" value of

*x*, which turnes this expression into 0. Or you can plug all the solutions into the original equation to see if all the denominators are Ok.

P.S. In different types of the questions, when you do not solve an equation but you are asked to simplify a formula, it is assumed that all the denominators are Ok.