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**Unformatted text preview: **Lecture 4: Section A.4 Rational Expressions Def. A rational expression is the quotient of two polynomials. The domain of an expression is the set of real numbers for which the expression is defined. ex. Find the domain. 1) 2 u1D465 5 − 6 u1D465 − 1 2) √ u1D465 + 3 3) u1D465 − 1 u1D465 + 5 Simplifying Rational Expressions A fraction is in simplest form if its numerator and denominator have no common factors. Use the Cancellation Property: u1D44E ⋅ u1D450 u1D44F ⋅ u1D450 = u1D44E u1D44F if u1D450 ∕ = 0 ex. Simplify: u1D465 3 − 4 u1D465 u1D465 2 − u1D465 − 2 and find its domain. Domain: Multiplying and Dividing Rational Expressions Recall: u1D44E u1D44F ⋅ u1D450 u1D451 = u1D44Eu1D450 u1D44Fu1D451 u1D44E u1D44F ÷ u1D450 u1D451 = u1D44E u1D44F ⋅ u1D451 u1D450 ex. u1D465 2 + 2 u1D465 − 3 u1D465 2 + 8 u1D465 + 16 ⋅ 3 u1D465 + 12 u1D465 − 1 ex. 4 − u1D465 u1D465 4 − 16 ÷ u1D465 2 − 3 u1D465 − 4 u1D465 2 + 5 u1D465 + 6 Adding and Subtracting Rational Expressions...

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