Addition and Subtraction of Rational Algebraic Expression

Math Lesson

ADDITION & SUBTRACTION: RATIONAL EXPRESSIONS

Adding and subtracting rational algebraic expressions. Just like regular fractions, they need a common denominator!

To add or subtract rational expressions, they MUST have the SAME denominator. If they are different, find the LCD (Least Common Denominator) first!
ac ± bc = a ± bc
Concept Explanation

Adding and subtracting rational expressions is similar to adding and subtracting fractions. If they have the same denominator, just add or subtract the numerators and copy the denominator. If they have different denominators, you must find the LCD to make them the same.

Formula / Rule

1. Same Denominator: ax + bx = a + bx
2. Different Denominators: Find the LCD. Multiply the numerator and denominator of each fraction by the necessary factor to make the denominators the same, then add or subtract.

4 Similar Worked Examples
Example 1: Add 3x + 2y
Denominators are x and y. LCD is xy.
Multiply first fraction by y, second by x:
3yxy + 2xxy
Add numerators: 3y + 2xxy
Example 2: Add 5a + 4b
Denominators are a and b. LCD is ab.
Multiply first fraction by b, second by a:
5bab + 4aab
Add numerators: 5b + 4aab
Example 3: Add 7m + 2n
Denominators are m and n. LCD is mn.
Multiply first fraction by n, second by m:
7nmn + 2mmn
Add numerators: 7n + 2mmn
Example 4: Add 1p + 8q
Denominators are p and q. LCD is pq.
Multiply first fraction by q, second by p:
qpq + 8ppq
Add numerators: q + 8ppq
Guided Practice

Try It Yourself!

Answer all 3 guided questions. Hints and solutions are available if you need them!

Mastery Check

Quick Quiz Time!

Answer all 10 questions in one go. Good luck!

Please answer ALL questions before submitting!
0/10

Made for students who want to master Addition & Subtraction of Rational Algebraic Expressions