1140 L4 - Lecture 4: Section A.4 Rational Expressions Def....

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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 de±ned. ex. Find the domain. 1) 2 x 5 ± 6 x ± 1 2) p x + 3 3) x ± 1 x + 5
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Simplifying Rational Expressions A fraction is in simplest form if its numerator and denominator have no common factors. Use the Cancellation Property: a ± c b ± c = a b if c 6 = 0 ex. Simplify: x 3 ² 4 x x 2 ² x ² 2 and ±nd its domain. Domain: Multiplying and Dividing Rational Expressions Recall: a b ± c d = ac bd a b ³ c d = a b ± d c
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ex. x 2 + 2 x ± 3 x 2 + 8 x + 16 ² 3 x + 12 x ± 1 ex. 4 x ± x 2 x 3 ± 64 ³ x x 2 + 4 x + 16
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Adding and Subtracting Rational Expressions Least Common Denominator (LCD) is the least common multiple (LCM) of the denominators. To ±nd it: 1. Factor each denominator completely. 2. The LCD is the product of each prime factor of the denominators, with each factor raise to its highest power in any denominator.
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1140 L4 - Lecture 4: Section A.4 Rational Expressions Def....

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