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**11-2 Rational Expressions**

Algebra Glencoe McGraw-Hill Linda Stamper

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**A rational number is a number that can be written as the**

quotient of two integers, such as A fraction whose numerator and denominator are nonzero polynomials is a rational expression. Because a rational expression involves division, the denominator may not equal zero. Any values of a variable that result in a denominator of zero must be excluded from the domain of that variable. These are called excluded values of the rational expression. Excluded values must always be determined from the original denominator.

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**State the excluded value for the rational expression.**

To find the excluded value set the denominator equal to zero and solve. Excluded value is 6. Set the denominator equal to zero. Factor and solve. 6 -2 –3 -5 Excluded values are 2 and 3.

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**Can you factor out a greatest monomial factor?**

State the excluded value for each rational expression. Example 1 Example 2 -3, 3 Example 3 Example 4 36 6 -9 –4 3 2 Can you factor out a greatest monomial factor? 5 -13 9, 4

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Simplifying a rational expression is similar to simplifying fractions because the variables in a rational expression represent real numbers. To simplify a rational expression, factor the numerator and denominator and then divide out any common factors. A rational number is in simplest form if its numerator and denominator have no factors in common other than 1. To understand today’s lesson, you MUST know the difference between factors and terms. Factors are values that are multiplied. Terms are values that are added or subtracted.

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**You can cancel (divide out) factors but not terms.**

Simplify the rational expression if possible. You can cancel (divide out) factors but not terms.

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**Simplify the expression. State the excluded value of the variable.**

18 1 The problem. Reduce the coefficients. Reduce the variables. Simplify. State the excluded value. Answer line

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**Simplify the expression. State the excluded value of the variable.**

1 Factor out a GCF. State the excluded value. 6

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**State the excluded value. 3**

Simplify the rational expression. State the excluded value of the variable. 1 Factor. State the excluded value. 3 Excluded values must always be determined from the original denominator.

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**Remember you can cancel (divide out) factors but not terms.**

Simplify the rational expression. State the excluded values of the variable. 1 1 / Ex. 5 Ex. 6 / 2 8 Excluded value is 0. Excluded value is 0. / 1 Ex. 8 Ex. 7 / Excluded values are 0 and -5. 0, -5 Remember you can cancel (divide out) factors but not terms. Answer line Excluded value is -3.

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**Simplify the rational expression**

Simplify the rational expression. State the excluded values of the variable. Example 9 Example 10 Example 11 Example 12 Example 13 Example 14

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**Simplify the rational expression**

Simplify the rational expression. State the excluded values of the variable. Example 9 Example 10 3 1 / / Factor out a GCF. Excluded value is ½. Excluded value is 5. Excluded values must always be determined from the original denominator.

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**Notice there are no parentheses in this answer!**

Simplify the rational expression. State the excluded values of the variable. Example 11 Example 12 1 1 Excluded value are 6 and 2. Excluded value are 7 and -4. Notice there are no parentheses in this answer!

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**Simplify the rational expression**

Simplify the rational expression. State the excluded values of the variable. Example 13 Example 14 1 1 1 Excluded value are Excluded value are 0 and 4. Notice there are no parentheses in this answer! Leave the answer in factor form!

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Homework 11-A2 Pages # 15–17,24–39,57-60.

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