Simplify, Simplify, Multiply & Multiply &

Divide Rational Divide 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.

How can I How can I simplify?simplify?

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

Divide the Divide the PolynomialPolynomial

Multiply Rational Multiply Rational FunctionsFunctions

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)

Divide Rational Functions “Keep Divide Rational Functions “Keep Change Flip!”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)

Multiply or Divide Rational Multiply or Divide Rational FunctionsFunctions

22 3 2 7 2111. 12.

3 2 10 5 2 5 2

x x x

x x x x