ALGEBRA I Chapter 6 Section 6
Alg 2: Unit 2
What is a RATIONAL EXPRESSION?
A RATIONAL EXPRESSION is an algebraic FRACTION whose numerator and denominator are polynomials.
What are EXCLUDED VALUES a rational expression? (Never divide by a ZERO)
EXCLUDED VALUES are any values for the variable that results in a denominator equal to zero.
To Find Excluded Values: Set DENOMINATOR = 0 and solve the equation .
(Hint: Factor Denominator as needed to solve)
1) [pic]
2) [pic]
3) [pic]
4) [pic]
5) [pic]
6) [pic]
7) [pic]
8) [pic]
How do you simplify rational expressions? (REDUCE FRACTIONS)
Step #1: FACTOR the Numerator and the Denominator
Step #2: CANCEL any common factors in both numerator and denominator or apply laws of exponents
HELPFUL Property of –1: GCF of -1 will make terms look alike ( [pic]
1) [pic]=
2) [pic]=
3) [pic]
Simplify Rational Expressions Continued
4) [pic]
5) [pic]
6) [pic]
7) [pic]
8) [pic]
9) [pic]
10) [pic]
11) [pic]
PRACTICE PROBLEMS: State the excluded values and then simplify, if possible
1) [pic]
2) [pic]
3) [pic]
4) [pic]
5) [pic]
6) [pic]
7) [pic]
8) [pic]
9) [pic]
Alg 2: Unit 2
MULTIPLYING RATIONAL EXPRESSIONS:
Step #1: FACTOR the Numerators and Denominators of each fraction
Step #2: Make ONE FRACTION with ALL Numerators and ALL Denominators to
(Use Parentheses)
Step #3: SIMPLIFY by canceling any common factors
EXAMPLES: Simplify each of the following rational expression multiplications
1) [pic]
2) [pic]
3) [pic]
4) [pic]
5) [pic]
6)[pic]
7) [pic]
8) [pic]
9) [pic]
10) [pic]
11) [pic]
PRACTICE PROBLEMS: Simplify the multiplications
1) [pic]
2) [pic]
3) [pic]
4) [pic]
5) [pic]
6) [pic]
Alg 2: Unit 2
DIVIDING RATIONAL EXPRESSIONS:
KEEP, CHANGE, FLIP ( Simplify
Step #1: CHANGE Division into Multiplication by the RECIPROCAL of the divisor
▪ Reciprocal of fraction [pic] (FLIP)
Step #2: FACTOR the Numerators and Denominators of each fraction
Step #3: MULTIPLY ALL Numerators and ALL Denominators to make a one fraction (use Parentheses)
Step #4: SIMPLIFY by canceling any common factors
EXAMPLES: Simplify each of the following rational expression divisions
1) [pic]
Reciprocal of [pic]: _________
Keep, Change, Flip
2) [pic]
Reciprocal of [pic]: _________
Keep, Change, Flip
3) [pic]
4) [pic]
5) [pic]
6) [pic]
7) [pic]
8) [pic]
9) [pic]
PRACTIVE PROBLEMS: Simplify the quotient
1) [pic]
2) [pic]
3) [pic]
4) [pic]
5) [pic]
6) [pic]
7) [pic]
8) [pic]
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