PREC11 Unit5 notes

# 25 63 o you can multiply the numerators and multiply

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Unformatted text preview: G RATIONAL EXPRESSIONS Multiplying rational expressions uses the same methods as when multiplying fractions. example: Evaluate 42 10 ; simplify your answer. 25 63 o You can multiply the numerators and multiply the denominators 420 1575 and then simplify OR o You can reduce the common factors from the numerators and (2)(3)(7) (2)(5) denominators and then multiply (5)(5) (3)(3)(7) 2 2 5 3 4 15 examples: State the restrictions on the variable(s) and then simplify. a) solutions 75 p 6 2qr 2 4 qr 15 p 2 p ≠ 0, q ≠ 0, r ≠ 0 5 p4 r 2 1 5 p4 r 2 b) x2 − 4 4 x − x2 2 x − 3x − 4 x 2 + 2 x ( x + 2)(x − 2) − x( x − 4) ⋅ x( x + 2) ( x + 1)(x − 4) x ≠ −2, x ≠ −1, x ≠ 0, x ≠ 4 (x − 2) − 1 ⋅ (x + 1) 1 − x − 2 or 2 − x x +1 x +1 These results mean that: 75 p 6 2qr 2 5 p4 r 4 qr 15 p 2 will equal 2 for all values of p, q, and r unless p, q, or r is 0; x2 − 4 x2 − 4 x 2 2 will equal − x − 2 for all values of x except −2, −1, 0, and 4. x +1 x − 3x − 4 x + 2x Unit 5: Day 3 notes - Multiplying and Dividing Rational Expressions Page 2 of 2 DIVIDING RATIONAL EXPRESSIONS Dividing rational expressions uses the same methods as when dividing fractions. example: Evaluate 11 ÷ 33 ; simplify your answer. 16 10 o Dividing by 33 is equivalent to multiplying by its reciprocal. 11 × 10 10 16 33 11 (2)(5) o Multiply and simplify. = 35 = 5 4 (3)(11) 24 2 2 (3) examples: State the restrictions on the variable(s) – remember that dividing by 0 is not permissible; and then simplify. a) 6 xy z 3 4 ÷ 9 x2 z b) x+6 x ÷ ( x + 6)( x − 3) ( x − 3)2 x ≠ 0, z ≠ 0 solutions x+6 ÷2x x + 3 x − 18 x − 6x + 9 2 6 xy z 2 3 4 z 9x 2y x ≠ −6, x ≠ 0, x ≠ 3 ( x − 3)2 x+6 ⋅ x ( x + 6)( x − 3) 3x 3 z x−3 x exercises: State the restrictions on the variable(s) and then simplify. a) 2 x2 − 5 x − 3 2 x2 + 3 x − 2 2 2 x − 5 x + 2 x2 − 4 x + 3 b) t 2 + 4t + 4 t −2 3t + 6 2 t − 5t + 6 1)( + 2) [Answers: x≠ 1 , x≠1, x≠2, x≠3, (2xx−+2)(xx− 1) ; t≠−2, t≠2, t≠3, (t + 2)(t − 3) ] 2 ( 3 PRE-CALCULUS 11 Unit 5...
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