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Section 6.1 Rational Expressions

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OBJECTIVES Determine the values that make a rational expression undefined. A

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**OBJECTIVES Build fractions.**

Reduce (simplify) a rational expression to lowest terms. C

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**RULES Avoiding Zero Denominators**

The variables in a rational expression must not be replaced by numbers that make the denominator zero.

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RULES Fundamental Rule of Rational Expressions

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**PROCEDURE Reducing Rational Expressions to Lowest Terms**

Write the numerator and denominator of the expression in factored form.

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**PROCEDURE Reducing Rational Expressions to Lowest Terms**

Find the factors that are common to the numerator and denominator.

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**PROCEDURE Reducing Rational Expressions to Lowest Terms**

Replace the quotient of the common factors by the number 1 since

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**PROCEDURE Reducing Rational Expressions to Lowest Terms**

Rewrite the expression in simplified form.

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RULE Quotient of Additive Inverses

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**Section 6.1 Exercise #1 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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**Let’s work Exercise #19 from Section 5.1**

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**Section 6.1 Exercise #2 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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**Let’s work Exercise #19 from Section 5.1**

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**Section 6.1 Exercise #3 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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**Let’s work Exercise #19 from Section 5.1**

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Section 6.2 Rational Expressions

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**OBJECTIVES Multiply two rational expressions.**

Divide one rational expression by another. B

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RULE Multiplying Rational Expressions

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**PROCEDURE Multiplying Rational Expressions**

Reduce each expression if possible. Multiply the numerators to obtain the new numerator.

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**PROCEDURE Multiplying Rational Expressions**

Multiply denominators to obtain new denominator. Reduce if possible.

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RULE Dividing Rational Expressions

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**Section 6.2 Exercise #6 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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**Section 6.2 Exercise #8 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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Section 6.3 Rational Expressions

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OBJECTIVES Add and subtract rational expressions with the same denominator. A

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OBJECTIVES Add and subtract rational expressions with different denominators. B Solve an application. C

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PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. Find the LCD.

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PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. Write all fractions as equivalent ones with LCD as the denominator.

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PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. Add or subtract numerators, keep denominators.

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PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. Reduce if possible.

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**Section 6.3 Exercise #11 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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**Section 6.3 Exercise #12 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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Section 6.4 Rational Expressions

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OBJECTIVE Simplify a complex fraction using one of two methods. A

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**DEFINITION Complex Fraction**

A fraction with one or more fractions in its numerator, denominator or both.

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**PROCEDURE Simplifying Complex Fractions**

Multiply numerator and denominator by the LCD of the fractions involved, or

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**PROCEDURE Simplifying Complex Fractions**

Perform operations indicated in numerator and denominator, then divide simplified numerator by simplified denominator.

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**Section 6.4 Exercise #13 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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Section 6.5 Rational Expressions

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OBJECTIVES Solve equations that contain rational expressions. A

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OBJECTIVES B Solve a rational equation for a specified variable.

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**LEAST COMMON MULTIPLE Multiplying each side of the equation**

by L is equivalent to multiplying each term by L.

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**Section 6.5 Exercise #17 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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**Section 6.5 Exercise #18 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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Section 6.6 Rational Expressions

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OBJECTIVES Solve proportions. A Solve applications. B

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RULE Cross Products

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**Section 6.6 Exercise #19 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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**Section 6.6 Exercise #21 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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**Section 6.6 Exercise #22 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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**Section 6.6 Exercise #25 Chapter 6 Rational Expressions**

Let’s work Exercise #19 from Section 5.1

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