Video: Simplifying Rational Expressions

Fully simplify (𝑥(𝑥 + 3))/((𝑥 + 2)(𝑥 + 3)).

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Video Transcript

Fully simplify 𝑥 multiplied by 𝑥 plus three divided by 𝑥 plus two multiplied by 𝑥 plus three.

In order to simplify any algebraic fraction written in this form, we need to cancel like terms. If there is a term that appears on the numerator and denominator of the fraction, it can be cancelled. In this case, we have 𝑥 and 𝑥 plus three on the numerator. We have 𝑥 plus two and 𝑥 plus three on the denominator. As 𝑥 plus three appears in the numerator and denominator, this can be cancelled.

𝑥 plus three divided by 𝑥 plus three is equal to one. We are therefore left with 𝑥 divided by or over 𝑥 plus two. The expression 𝑥 multiplied by 𝑥 plus three divided by 𝑥 plus two multiplied by 𝑥 plus three fully simplified is equal to 𝑥 divided by 𝑥 plus two.

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