25 63 o you can multiply the numerators and multiply

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 02/16/2014 for the course MATH Pre-Calcul at Holy Cross Regional High School.

Ask a homework question - tutors are online