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**Rational Algebraic Expressions**

Objective: To simplify rational algebraic expressions

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**Rational Algebraic Expression**

Quotient of two algebraic expressions Example:

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**Simplify the following expression:**

start by factoring after the polynomials are factored you can “cancel” terms whose quotient is one

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**Finding domain and zero’s**

Given: Start by factoring the numerator and denominator. The domain of the function is all reals except where the denominator equals zero x ≠ 0 x + 2 ≠ 0 x – 2 ≠ 0 x ≠ 0 x ≠ -2 x ≠ 2

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Zeros of the function The zeros of the function are where the numerator equals zero. 2x + 1 = 0 x – 2 = 0 x = -½ x = 2 Remember x = 2 is not in the domain so it cannot be a zero of the function.

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**Try These! Simplify 2x – 1 More try these!**

#5 Hint: add and subtract all missing terms

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Back to Try These!

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Back to Try These!

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Back to Try These!

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Back to Try These!

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Back to Try These!

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**Try These! Find the domain and zeros of the function**

D: x ≠ 0, x ≠ -4 zeros {2, -2} D: x ≠ -1/3 x ≠ -4 zeros {-3/2, -2} D: x ≠ -1 zeros {-2}

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Table of Contents Rational Expressions and Functions where P(x) and Q(x) are polynomials, Q(x) ≠ 0. Example 1: The following are examples of rational expressions:

Table of Contents Rational Expressions and Functions where P(x) and Q(x) are polynomials, Q(x) ≠ 0. Example 1: The following are examples of rational expressions:

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