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]

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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

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PRACTICE PROBLEMS: State the excluded values and then simplify, if possible

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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]

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11) [pic]

PRACTICE PROBLEMS: Simplify the multiplications

1) [pic]

2) [pic]

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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]

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PRACTIVE PROBLEMS: Simplify the quotient

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