By Charles Denlinger and Elaine Jacobson (Auth.)

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8. 9. 10. 11. 12. 13. 14. 15. 16. 17. WORKING WITH RATIONAL EXPRESSIONS The four multiplication same rules set 1. We restate fundamental operations of addition, subtraction, and division of rational fractions follow the forth for rational numbers in Table 2 of Chapter them here for algebraic fractions. MORE RULES FOR RATIONAL EXPRESSIONS (a) To multiply two algebraic fractions, simply multiply their numerators and multiply their denominators. Then reduce to lowest terms. (b) To divide two algebraic fractions, simply invert the divisor, and multiply using rule (a).

37. 38. 39. 40. i . [i - ( i . (i 51. 1 INTRODUCTION If 2 is substituted in the equation 3x- 2 = 4 the two sides become equal. We say that x = 2 is a solution of the equation. The following operations are helpful for finding the solu tions of an equation: I. II. The same quantity may be added to or subtracted from both sides of an equation. Both sides of an equation may be multiplied (or divided) by the same non-zero quantity. EXAMPLE 1 Solve for x: 4x- 7 5 4x 12 x 3 We have solved for x. (adding 7 to both sides) (dividing both sides by 4) 52.

Lack of this important skill is one of the most frequent causes of agony arid frustration in calculus (and related) courses. The important principles are few in number, and are not new. Indeed they are simply restatements of the rules given for rational numbers in Table 2 of Chapter 1. Rules for Rational Expressions: (a) We may multiply (or divide) both the numerator and the denominator of a rational expression by the same (non-zero) polynomial. (b) To reduce a rational expression to lowest terms we factor the numerator and the denominator, and cancel out any factors common to both.