SIMPLIFYING RATIONAL EXPRESSIONS

Transcription

1 MATH 65 LAB RATIONAL EXPRESSIONS and EQUATIONS Name Instruct: T. Henson Purpose: Practice in simplifying rational s and in perfming operations with rational s and in solving rational s. To develop understanding of the differences and similarities between these various processes. Learning Goals: Symbolic and numerical representation; quantitative reasoning; communication. Simplify rational s; know how to tell a rational is in simplest fm. Multiply divide rational s and write the result in simplest fm. Add subtract rational s with like unlike denominats and write the result in simplest fm. Solve rational s Describe the processes f simplifying, multiplying, dividing, and adding and subtracting rational s. Describe the process f solving rational s Distinguish between rational s and s. Distinguish between the methods used to simplify rational s, perfm rational operations and solve rational s A. SIMPLIFYING RATIONAL EXPRESSIONS. Simplify each rational. Show all steps of your wk/thinking. NO CREDIT f answers without suppting wk x 7x 8x 4 3. x 7x+ 1 x 16 B. MULTIPLYING RATIONAL EXPRESSIONS. Multiply the rational s and write the result in simplest fm. Show all steps of your wk/thinking. NO CREDIT f answers without suppting wk. 1. x 3x 10 15x 5x 3x 15

2 Page of 7. x x 3 3x 11x 0 3x + 7x x C. DIVIDING RATIONAL EXPRESSIONS. Divide the rational s and write the result in simplest fm. Show all steps of your wk/thinking. NO CREDIT f answers without suppting wk m m m m m m m D. ADDING AND SUBTRACTING RATIONAL EXPRESSIONS. Perfm the indicated addition subtraction of rational s and write the result in simplest fm. Show all steps of your wk/thinking. NO CREDIT f answers without suppting wk. 1. x + 6x 7x x+ 5 x+ 5. 5a 1 3a a a a a

3 Page 3 of 7 3. m 4 + m m+ 4. y 4 y + y + y E. SOLVING RATIONAL EQUATIONS. Solve each rational and check your solution(s). Indicate any extraneous solutions. Show all steps of your wk/thinking. NO CREDIT f answers without suppting wk. 1. 3x 1 7 Check: + = 4x 3x 6x

4 Page 4 of 7. 3 a + = a 3 a 3 Check: F. EXPRESSIONS vs. EQUATIONS 1. Describe in your own wds the key steps f carrying out each of the following processes: a. The process of simplifying a rational b. The process of multiplying and/ dividing rational s c. The process of adding and/ subtracting rational s d. The process of solving a rational.

5 Page 5 of 7. Referring to the four processes stated in problem 1, a. In which of the four processes is it necessary to find the lowest common denominat (LCD)? b. How is the LCD used when adding subtracting rational s? c. How is the LCD used when solving rational s? 3. In each problem below, indicate whether the mathematical statement in the problem is an an. If it is an, carry out any indicated operations and simplify, if possible. If it is an, find all solutions, if any, and indicate any extraneous solutions. (a) y + 3y 3y 9 y + 3 (b) x 4 + = x 1 3 x 1

6 Page 6 of 7 (c) r r r r 5 r 5 (d) x + 7x+ 10 6x 6 3x+ 6 x + x 15 (e) x 1 + = x + 1 x + 1 (f) 4 x x x x x x

7 Page 7 of 7 (g) c+ c + c (h) = m m+ m + m