University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

420

Pages:

1
Author:

grosikesf4

Mini-Lecture 7.1 Simplifying Rational Expressions Learning Objectives: 1. Find the value of a rational expression given a replacement number. 2. Identify values for which a rational expression is undefined. 3. Simplify or write rational expressions in lowest terms. a −a a = 4. Write equivalent rational expressions of the form − = . b b −b Examples: 1. Find the value of the expression for the given value (s). a) x+4 ;x=4 x−2 b) y2 ; y=5 y−3 c) x 2 + 5x − 2 x2 − x − 2 ; x = −3 2. Find any numbers for which each rational expression is undefined. a) 7 4a b) 3y3 y − 5y 2 c) x 2x − 7x − 4 2 3. Simplify each expression. a) d) ( y + 3)( y − 1) ( y − 1)( y + 5) 6x − 12 3x 2 − 12 b) e) 6−a a −6 y 2 + 8y + 15 y 2 + 9y + 18 c) f) −2x − 2y x+y x 2 − xy + 5x − 5y x 2 + 5x 4. List four equivalent forms for each rational expression. a) − x−2 x+5 b) − y+3 y − 11 c) − 5y + 2 3y − 1 Teaching Notes: • • • Some students need a review of simplifying numerical fractions before applying to rational expressions. Many students need to be reminded to factor completely before simplifying. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. y+3 2 ; 3b) -1; 3c) -2; 3d) ; x+2 y+5 y+5 x− y −( x − 2) 2 − x x−2 x−2 −( y + 3) − y − 3 y+3 y+3 ; 3f) ; 4a) ; 4b) ; , , , , , , 3e) x x + 5 x + 5 − ( x + 5) − x − 5 y − 11 y − 11 − ( y − 11) 11 − y y+6 Answers: 1a) 4; 1b) 25/2; 1c) -4/5; 2a) 0; 2b) 0, 5; 2c) -1/2, 4; 3a) 4c) −(5 y + 2) −5 y − 2 5 y + 2 5 y + 2 , , , 3y −1 3 y − 1 − ( 3 y − 1) 1 − 3 y