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Adding & Adding & Subtracting Subtracting
Rational Rational ExpressionsExpressions
VocabularyVocabulary• Rational Expression Rational Expression - An expression
that can be written as a ratio of 2 polynomials
• Excluded Value Excluded Value – A number that makes a rational expression undefined.
• Simplest form of a rational expression Simplest form of a rational expression – Numerator and denominator have no factors in common other than 1.
Ex.Ex. Find the excluded values of the Find the excluded values of the expression.expression.
6
14
x
x
9 1
5
x
x
1. 2.
How do we add/sub fractions with How do we add/sub fractions with likelike denominators?denominators?
Ex. Add/Sub Rational Functions (LIKE Denominators)
3 4 2 9 6 8 3 6 5 2 513. 14. 15. 16.
8 8 1 1 4 4 1 1
x x x x
x x x x x x x x
1. Add/Sub Numerator
2. Leave Denominator
How do we add/sub fractions with unlike denominators?
Ex. Add/Sub Rational Functions (UNLIKE Denominators)
3 3 4
5 2 1 317. 18.
36 4 3 4x x x x
1. Get Common Denominator
2. Follow Add/Sub Steps
Ex. Add/Sub Rational Functions (UNLIKE Denominators)
7 1 9 1519. 20.
8 3 1 3 1
x x
x x x x
EX.EX. Simplify the expression. Simplify the expression. State the excluded value.State the excluded value.
2 2
2 3 3 4
18 303. 4.
6 3
x y z
x x y z
1. Divide Numbers
2. Simplify Variables
EX.EX. Simplify the expression. Simplify the expression. State the excluded value.State the excluded value.
212 6 4( 3)5. 6.
24 6( 3)
x x x
x x
Ex. Multiply Rational Functions
2 3 2 4 3
2 2 4
14 9 15 217. 8.
3 2 3 5
x x y z x y
x x y yz
1. Multiply Numerators
2. Multiply Denominators
3. Simplify (See previous slide)
Ex. Divide Rational Functions “Keep Change Flip!”
4 3 3 2 4 3
2 2 4
15 3 5 159. 10.
6 2 4 6
y y a b c a b
a b ac
1. Change Division to Multiplication
2. Flip the 2nd Fraction
3. Simplify (See previous slide)
Ex. Multiply or Divide Rational Functions
22 3 2 7 2111. 12.
3 2 10 5 2 5 2
x x x
x x x x
HOMEWORK!
Pg. 162 #5Pg. 163 #1-3, 10
Pg. 167 #1, 2, 10, 11Pg. 173 #1-6, 13-15
