Video: Simplifying Rational Expressions

Fully simplify (𝑥 − 3)³/((𝑥 − 3)³ (𝑥 + 8)).

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Video Transcript

Fully simplify 𝑥 minus three all cubed divided by 𝑥 minus three cubed multiplied by 𝑥 plus eight.

So when you’re actually looking to simplify an expression like this, what you need to do is look at the numerator and the denominator and see if there are any common factors. Well, in this example, we actually see some very obvious factors that are the same in our numerator and denominator, because actually we have 𝑥 minus three all cubed on our numerator and 𝑥 minus three all cubed on our denominator.

So therefore, if we actually divide the numerator and the denominator by 𝑥 minus three all cubed, what we’re gonna be left with is one as the numerator. That’s because 𝑥 minus three all cubed divided by 𝑥 minus three all cubed is one. And on the denominator, we’re just gonna have 𝑥 plus eight. And that’s again because if we divided 𝑥 minus three all cubed multiplied by 𝑥 plus eight by 𝑥 minus three all cubed, then we just have one multiplied by 𝑥 plus eight, which gives us 𝑥 plus eight.

So therefore, we can say that if we fully simplify 𝑥 minus three all cubed over 𝑥 minus three all cubed multiplied by 𝑥 plus eight, we get one over 𝑥 plus eight.

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