Video: Simplifying Rational Expressions

Fully simplify (π‘₯ βˆ’ 2)Β²/((π‘₯ βˆ’ 2)(π‘₯ + 2)).

01:33

Video Transcript

Fully simplify π‘₯ minus two all squared over π‘₯ minus two multiplied by π‘₯ plus two.

So, the first thing we want to do with this question is rewrite π‘₯ minus two all squared over π‘₯ minus two multiplied by π‘₯ plus two. And, we’re gonna rewrite it using the fact that π‘₯ minus two all squared means π‘₯ minus two multiplied by π‘₯ minus two. So, if we rewrite it using that, what we get is that it’s equal to π‘₯ minus two multiplied by π‘₯ minus two over π‘₯ minus two multiplied by π‘₯ plus two.

So next, what we need to do is look at the numerator and denominator and see if there are any common factors. And, there are because we can see that on the numerator we have π‘₯ minus two multiplied by π‘₯ minus two. So, there are two factors; they’re both π‘₯ minus two. And then on the denominator, one of the factors is also π‘₯ minus two. So then, what we can do is divide the numerator and denominator by a common factor, if there is. And that common factor, as we said, was π‘₯ minus two. So, when divided by π‘₯ minus two, we can cancel one of the π‘₯ minus two factors out from the numerator and the one from the denominator.

So therefore, when we do that, we’re left with π‘₯ minus two over π‘₯ plus two , and this cannot be simplified any further. So therefore, we can say that if we fully simplify π‘₯ minus two all squared over π‘₯ minus two multiplied by π‘₯ plus two, then we get π‘₯ minus two over π‘₯ plus two.

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