Adding and Subtracting Rational Expressions

Explore least common denominator, equivalent numerators, final simplification.

Lesson 3 of 53 parts Practice Flashcards

1/3

Least Common Denominator

Objective: Explain least common denominator and use it to solve or interpret a problem.

Factor denominators and include each distinct factor to its highest necessary power in a least common denominator; identify excluded inputs first. Factoring reveals shared factors and avoids needless multiplication.

Worked examples

Try itAdding and Subtracting Rational Expressions — practice 1.1: Find the least common denominator of 1/(x−3) and 1/(x−5), assuming 3≠5. How many distinct linear factors?Show answer

Step 1: The denominators are x−3 and x−5. Step 2: They are distinct linear factors. Step 3: The least common denominator contains two such factors.

Swipe sideways to move between sections

Least Common Denominator

Objective: Explain least common denominator and use it to solve or interpret a problem.

Worked examples

Try itAdding and Subtracting Rational Expressions — practice 1.1: Find the least common denominator of 1/(x−3) and 1/(x−5), assuming 3≠5. How many distinct linear factors?Show answer

Step 1: The denominators are x−3 and x−5. Step 2: They are distinct linear factors. Step 3: The least common denominator contains two such factors.

Equivalent Numerators

Objective: Explain equivalent numerators and use it to solve or interpret a problem.

Multiply each fraction by a form of one to reach the common denominator; then combine numerators, keeping the common denominator unchanged. Addition combines numerators over a shared denominator.

Worked examples

Try itAdding and Subtracting Rational Expressions — practice 2.1: Find 1/4+1/3 as a fraction.Show answer

Step 1: Use common denominator 12. Step 2: Convert to 3/12+4/12. Step 3: Add to get 7/12.

Final Simplification

Objective: Explain final simplification and use it to solve or interpret a problem.

After combining, factor the resulting numerator and cancel valid common factors, while retaining the exclusions from original terms. An originally undefined input stays invalid.

Worked examples

Try itAdding and Subtracting Rational Expressions — practice 3.1: Find 1/2+1/4 as a fraction.Show answer

Step 1: Use common denominator 8. Step 2: Convert to 4/8+2/8. Step 3: Add to get 3/4.

You finished the reading!

Lock it in with a few practice questions, then move on to the next lesson.

Practice Next lesson

Previous lessonMultiplying and Dividing Rational Expressions Next lessonGraphing Rational Functions