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Chapter 7 Rational Expressions and Equations Lesson 7-1a Simplifying Rational Expressions

Objective: Students will learn the definition of a rational expression and the significance of rational expressions and dividing by zero. Students will learn what the domain of a rational expression is and how to calculate it. Students will learn techniques of how to simplify rational expressions using factoring.

What You Will Learn  Find the domain of a rational expression  Simplify rational expressions

Rational Expressions and Their Domains A rational expression is a fraction whose numerator and denominator are polynomials. Some examples are and The domain of a rational expression is the set of all real numbers for which it is defined.

Rational Expressions and Their Domains To find the values to exclude from the domain, set the denominator equal to zero and find the solution(s) of that equation. The domain answers the question, “What numbers are possible for x?”

Example 2-1a Answer: b cannot equal –7. State the excluded value of Check: Division by 0 is impossible. Since division by 0 is impossible, find when b + 7 is 0.

Example 2-2a or Answer: a cannot equal –3 or 4. State the excluded value of

Example 2-4a Simplify State the excluded values of x and y.

Example 2-6a 1 1 SimplifyState the excluded values of x. Answer: Excluded values are x cannot = {9, -4} Always find the Excluded values first!!! x cannot = {-4}

Example 2-5a 1 1 Simplify Answer: State the excluded values of x. Excluded values are x cannot = {7, -5} x cannot = {7}

Example 2-1b Answer: State the excluded value of The excluded value is y cannot = {-3}

Example 2-2b Answer: State the excluded value of The excluded values are x cannot = {2, 3}

Example 2-4b Simplify Answer: The excluded values are a and b cannot = {0} a cannot = {0}

Example 2-5b Simplify Answer: State the excluded values The excluded values are c cannot = {6, -1} c cannot = {6}

Example 2-6e Answer: SimplifyState the excluded values of w. The excluded values are w cannot = {-8, 2} w cannot = {2}

Lesson Summary: Objective: Students will learn the definition of a rational expression and the significance of rational expressions and dividing by zero. Students will learn what the domain of a rational expression is and how to calculate it. Students will learn techniques of how to simplify rational expressions using factoring.

Preview of the next Lesson: Objective: Students will solve real world word problems involving simplifying rational expressions.

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