Download Excluded Values of Rational Expressions

[Algebra 1 (X)]
12.2: Rational Expressions
HCPS III:  Standard 10: Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations.  Benchmark MA.AI.10.3: Justify the steps used in simplifying expressions and solving equations and inequalities. Goals: 
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Identify values excluded from the domain of a rational expression. Simplify rational expressions Excluded Values of Rational Expressions A rational expression is a fraction whose numerator and denominator are polynomials. Since rational expressions are essentially fractions, the denominator cannot equal zero. If the denominator is zero, the fraction is undefined. Excluded values of rational expressions are values of a variable that cause the denominator to equal zero. Example 1: One Excluded Value State the excluded value of each expression. ହ௠ାଷ
a.) ௠ି଺
b.) ସ௠ି଼
௠ାଶ
Example 2: Multiple Excluded Values State the excluded values of each expression. ௫ మ ିହ
a.) మ
௫ ିହ௫ା଺
௫ మ ାଵ
b.) మ ௫ ିଽ
Simplify Rational Expressions To simplify a rational expression, factor the numerator and denominator and then divide out any common factors. Example 3: Simplify Rational Expressions Involving Monomials Simplify the rational expression if possible. ି଻௔మ ௕య
a.) ଶଵ௔ఱ ௕
ହସ௭ య
b.) ଶସ௬௭
Example 4: Simplify Rational Expressions Involving Polynomials Simplify the expression if possible. ௫ మ ିଶ௫ିଵହ
a.) మ
௫ ି௫ିଵଶ
ଷ௫ିଽ
b.) మ
௫ ିହ௫ା଺
Example 5: Simplifying Rational Expression and Excluded Values Simplify the expression if possible. State the excluded values. ଷ௫ିଵହ
మ
௫ ି଻௫ାଵ଴