Fully simplify 𝑥 plus four times
𝑥 plus three over 𝑥 plus two times 𝑥 plus four.
Remember, to simplify fractions, we
divide the numerator and denominator by the greatest common factor of each. Let’s look carefully at the
numerator and denominator of our fraction. The factors of the numerator are 𝑥
plus four and 𝑥 plus three. Then the factors of the denominator
are 𝑥 plus two and 𝑥 plus four. We can therefore say that the
greatest common factor is 𝑥 plus four. It’s the only factor other than one
that these two expressions have in common.
So to simplify this algebraic
fraction, we’re going to divide through by 𝑥 plus four on both parts. 𝑥 plus four times 𝑥 plus three
divided by 𝑥 plus four leaves us with 𝑥 plus three on our numerator. Similarly, 𝑥 plus two times 𝑥
plus four divided by 𝑥 plus four leaves us with 𝑥 plus two on our denominator. That leaves us with 𝑥 plus three
over 𝑥 plus two. 𝑥 plus three and 𝑥 plus two are
now coprime. They share no other factors other
than one. So we’re finished. In its simplest form, our fraction
is 𝑥 plus three over 𝑥 plus two.