Adding Rational Expressions with Common Denominators

1
Adding Rational Expressions with Common
Denominators

• To add rational expressions with the same
  denominator, add numerators and place the sum
  over the common denominator. If possible,
  simplify.

2
Add
Step 1 Add numerators. Place the sum over the
common denominator.
Step 2 Combine like terms. Factor and simplify
if possible. This does not simplify.
3
Add
Step 1 Add numerators. Place the sum over the
common denominator.
Step 2 Combine like terms.
Step 3 Factor and simplify.
4
Subtracting Rational Expressions with Common
Denominators

• To subtract rational expressions with the same
  denominator, subtract numerators and place the
  difference over the common denominator. If
  possible, simplify.

5
Subtract
Step 1 Subtract numerators. Place the
difference over the common denominator.
Step 2 Remove parentheses, change the sign of
each term.
Step 3 Combine like terms.
Step 4 Factor and simplify.
6
Subtract
Step 1 NOTE The denominators are opposites.
Multiply the second expression by -1/-1.
Step 2 Subtract numerators. Place the
difference over the common denominator.
Step 3 Factor and simplify.
7
ReferenceBlitzer, Introductory and Intermediate
Algebra