Warm- upWarm- up
Factor completely:
4
4 3 2
16 64p
c c c c
Simplify, Multiply and Simplify, Multiply and Divide Rational Divide Rational
ExpressionsExpressionsObjectives:
•To simplify rational expressions, and•Simplify complex fractions
Rational algebraic expressionsRational algebraic expressions
A rational algebraic expression can be expressed as the quotient of two polynomials.
◦Note: The denominator can NEVER be 0.
Rational ExpressionRational Expression
Property: Let a, b, and c be expressions with and
Then the following property applies:
0b 0.c
ac
bc
Simplified Form of a Rational Simplified Form of a Rational ExpressionExpression
A rational expression is in SIMPLIFIED FORM if its numerator and DENOMINATOR have no common factors other than
1
procedureprocedure
1. Factor the numerator and denominator.
2. Divide out any factors that are common to both.
3. State the excluded values by setting the denominator =0 and solving.
Example: 2
2
7x x
x
BIG NO NOBIG NO NO
1. Factor the numerator and denominator.
2. Divide out any factors that are common to both.
3. State the excluded values by setting the denominator =0 and solving.
Example: 2
2
7x x
x
Simply rational expressionsSimply rational expressions
Example 1
2
2 ( 1)
( 1)( 4)
x x
x x
Simply rational expressionsSimply rational expressions
Example #2
2 2
2
2 ( 4)( 3).
8 ( 2)( 4)
a a b
ab a a
Simplify rational expressionsSimplify rational expressions
Example 3: Simplify:
2 4
3
3
2 6
a a
a a
Simplify rational expressionsSimplify rational expressions
Example 4: Simplify:
2
2
2 10
3 16 5
x x
x x
Multiply fractions/rational Multiply fractions/rational expressionsexpressions
Recall to multiply two fractions or rational expressions, you first multiply the numerators and then multiply the denominators.
3 2 3 10
4 15 5 9
MULTIPLYING PROCEDUREMULTIPLYING PROCEDURE
1. MULTIPLY THE NUMERATORS.
2. MULTIPLY THE DENOMINATORS.
3. WRITE THE NEW FRACTION IN SIMPLIFIED FORM.
Multiply rational expressionsMultiply rational expressions
Example 5: Multiply:
Recall to multiply two fractions or rational expressions, you first multiply the numerators and then multiply the denominators.
2 2
2 3
2 3
5 8
a bc
b c a
Multiply rational expressionsMultiply rational expressions
Example 6: Multiply:
Example 7: Multiply:
3
2
7 63
9 35
a b
b a
2
3 2 3
14 24
9 35
c d mn
m n cd
Multiply rational expressionsMultiply rational expressions
Example 8: Multiply:
2 2
2
3 3 20
4 5 3
a a a a
a a a
Dividing ProcedureDividing Procedure
1. Multiply by the reciprocal2. Simplify.
Divide rational expressionsDivide rational expressions
Example 9
2 2
2 4
8 2
15 5
x y xy
a b ab
Divide rational expressionsDivide rational expressions
Example 10: Divide: 2 3
3 2
14 35
9 24
c d cd
m n mn
Divide rational expressionsDivide rational expressions
Example 11: Divide: 2
2
2 8 2
4 3 3 3
x x x
x x x
Divide rational expressionsDivide rational expressions
Example 12: Divide:2 2
2 ( 2)
5 25
y y y
y y y
In groups of 4In groups of 4
Person 1: Write two rational expressions using the same variables
Person 2: Simplify the expressionPerson 3: Multiply the two expressionsPerson 4: Divide the two expressions
DISCUSSROTATE AND REPREAT
TOTDTOTD
Explain under what conditions a rational polynomial expression is not defined.
homeworkhomework
Kuta worksheet