College Algebra & Trigonometry, 2018a

62 CHAPTER 1. ALGEBRA REVIEW
1.7 Adding and Subtracting Rational Expressions
Just as we do with numerical fractions, we will need to have common denominators
in order to add or subtract algebraic fractions. When we add 1 2 + 1 , we make
3
a common denominator of 6 so that we can add them together.
1
2 + 1 3 = 1 2 ∗ 3 3 + 1 3 ∗ 2 2
= 3 6 + 2 6
= 5 6
Because the denominators, 2 and 3, are prime and don’t share any common factors,
the common denominator is simply 3 ∗ 2=6. We can see a similar result in
adding algebraic fractions.
Example
Add the fractions. Express your answer in lowest terms.
2
x + x
x − 3
2
x +
x
x − 3 = 2 x ∗ x − 3
x − 3 +
=
x
x − 3 ∗ x x
2(x − 3)
x(x − 3) + x ∗ x
x(x − 3)
=
2x − 6+x2
x(x − 3)
= x2 +2x − 6
x(x − 3)