Question Video: Simplifying Rational Expressions | Nagwa Question Video: Simplifying Rational Expressions | Nagwa

# Question Video: Simplifying Rational Expressions Mathematics

Fully simplify ((π₯ + 4)(π₯ + 3))/((π₯ + 2)(π₯ + 4)).

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### Video Transcript

Fully simplify π₯ plus four times π₯ plus three over π₯ plus two times π₯ plus four.

Remember, to simplify fractions, we divide the numerator and denominator by the greatest common factor of each. Letβs look carefully at the numerator and denominator of our fraction. The factors of the numerator are π₯ plus four and π₯ plus three. Then the factors of the denominator are π₯ plus two and π₯ plus four. We can therefore say that the greatest common factor is π₯ plus four. Itβs the only factor other than one that these two expressions have in common.

So to simplify this algebraic fraction, weβre going to divide through by π₯ plus four on both parts. π₯ plus four times π₯ plus three divided by π₯ plus four leaves us with π₯ plus three on our numerator. Similarly, π₯ plus two times π₯ plus four divided by π₯ plus four leaves us with π₯ plus two on our denominator. That leaves us with π₯ plus three over π₯ plus two. π₯ plus three and π₯ plus two are now coprime. They share no other factors other than one. So weβre finished. In its simplest form, our fraction is π₯ plus three over π₯ plus two.

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