Pre-Calculus 11 Notes

By: Gen L.

Lesson 2: Adding & Subtracting Rationals

Adding & Subtracting

• Since we're dealing with fractions, the same rules apply. One of the fundamental rules is that when adding or subtracting fractions, there must be a common denominator.
• Example:
  • .
• Example:

Finding a Common Denominator

• Finding a common denominator with variables is very similar to what you have already done.
• Example:

Example 4: Addition

1. • We have two we'll need to factor early on.
2. • Next, state the NPVs: , and determine LCD:
3. • FOIL :
4. • Rewrite the rational.

Example 4, cont.

5. • Combine like terms.
6. • Simplify numerator (Factor!)
7. • Simplify like terms.

Example 5: Subtraction

1. • Determine common denominator:
2. • State NPVs: and FOIL
3. • Rewrite the Rational
4. • Rewrite the Subtraction

Example 5, cont.

5. • Combine like terms
6. • If possible, simplify.
     • 13 is prime, so we can't.

Example 6: Recursion

1. • The bar means division, so rewrite horizontally.
2. • State NPVs: & Determine Common Denominator for each set: .
3. • Kiss and Flip, add another NPV: .
     • Why another NPV? Keep NPVs Up to Date. Any new denominator = new NPVs.

Example 6, cont.

4. • Old Denominators cross-cancel.
5. • Factor as needed.
6. • Combine like terms.

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