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Precalc0006to0010-page19 - different opinions as to what...

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(Section 0.9: Simplifying Algebraic Expressions) 0.9.1 SECTION 0.9: SIMPLIFYING ALGEBRAIC EXPRESSIONS LEARNING OBJECTIVES • Be able to use factoring and canceling (i.e., division) to simplify algebraic expressions. • Be able to rationalize the numerator or the denominator of a fraction containing radical(s). • Be aware of common errors when rewriting and simplifying expressions. PART A: DISCUSSION • The factoring techniques from Sections 0.7 and 0.8 will help us simplify fractions by canceling (i.e., dividing out ) common factors . • We can also re-express or simplify a fraction by rationalizing the numerator or the denominator. PART B: CANCELING COMMON FACTORS IN A FRACTION We are typically required to provide answers in simplified form. While there are
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Unformatted text preview: different opinions as to what that means, there is common agreement that factors (other than 1 and ± 1 ) that are common to both the numerator and the denominator of a fraction must be canceled (i.e., divided out ). WARNING 1 : Some instructors object to the term “canceling,” because students often abuse the idea by inappropriately and carelessly deleting matching expressions. Remember to rely on mathematical rules, not merely wishful thinking! Canceling Rule for Fractions As we simplify a fraction, we can “cancel”: a nonzero factor of the entire numerator with an equivalent factor of the entire denominator. • That is, we can divide the entire numerator and the entire denominator by equivalent nonzero factors ....
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