PREC11 Unit5 notes

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Unformatted text preview: – Day 4: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS (Part 1) ADDING AND SUBTRACTING RATIONAL EXPRESSIONS Adding and subtracting rational expressions uses the same methods as when adding and subtracting fractions. example: Evaluate 8 − 7 ; simplify your answer. 15 10 o You need common denominators; choose the lowest common denominator which would be the lowest common multiple of the denominators. 15 = (3)(5) and 10 = (2)(5) . The lowest common multiple will need the factors 2, 3, and 5; LCD = (2)(3)(5) = 30 . (8)(2) (7)(3) o Raise the fractions to higher terms. − (15)(2) (10)(3) 16 − 21 30 30 −5 o Subtract the numerators. 30 o Simplify. −1 6 example: Simplify. 2a − 3b − 3a − 2b 10a 25b solution exercise: Simplify 1 + 2x − 3 − x − 5 3 5x 6 x2 LCD = 50ab (2a − 3b)(5b) (3a − 2b)(2a) − (10a)(5b) (25b)(2a) 5b(2a − 3b) 2a(3a − 2b) − 50ab 50ab 5b(2a − 3b) − 2a(3a − 2b) 50ab 10ab − 15b2 − 6a2 + 4 ab 50ab −6a2 + 14 ab − 15b2 50ab [Answer: 4 x2 + 40 x − 15 30 x2 Unit 5: Day 4 notes - Adding and Subtracting Rational Expressions (Part 1) example: Simplify. 2 − 2m m m−5 solution Page 2 of 2 exercise: Simplify 2x − x − 1 x −2 x+7 LCD = m(m − 5) 2(m − 5) 2m(m) − m (m − 5) m (m − 5) 2(m − 5) − 2m2 m (m − 5) 2m − 10 − 2m2 m (m − 5) − 2m2 + 2m − 10 m (m − 5) [Answer: example: Simplify. t −1 − t2− 2 t + 5t + 4 t +t 2 solution x2 + 17 x − 2 ( x − 2)( x + 7) exercise: Simplify 2 − 21 x + 3x + 2 x + x −2 2 t −1 − t −2 (t + 1)(t + 4) t (t + 1) LCD = t(t + 1)(t + 4) t (t − 1) (t − 2)(t + 4) − t (t + 1)(t + 4) t (t + 1)(t + 4) t (t − 1) − (t − 2)(t + 4) t (t + 1)(t + 4) t 2 − t − (t 2 + 2t − 8) t (t + 1)(t + 4) t 2 − t − t 2 − 2t + 8 t (t + 1)(t + 4) −3t + 8 t (t + 1)(t + 4) [Answer: x−3 ( x − 1)( x + 1)( x + 2) PRE-CALCULUS 11 Unit 5 – Day 5: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS (Part 2) MODELLING BY ADDING AND SUBTRACTING RATIONAL EXPRESSIONS example: The cu...
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This document was uploaded on 02/16/2014 for the course MATH Pre-Calcul at Holy Cross Regional High School.

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