1 L1 § 1.1 Real numbers and their propertiesExpressions of the form ab. We will be dealing with fractional expressions on a regular basis. Here are two important questions: 1. When is the fractional expression undefined? Answer: When the denominator0b=(division by 0 is undefined). Note: As more situations arise, there will be more restrictions such as when taking square roots. 2. When is the fractional expression equal to zero? Answer: When the numerator0a=, provided the denominator 0b≠. A word of caution: 00is not a number! Therefore, a number that makes an expression equal to 00does notmake it equal to 0. 2 Example. a) Find the value of xso that 234xx−+is undefined. b) Find the value of xso that 2034xx−=+. Example. a) Find the value of xso that (3)x xx−is undefined. b) Find the value(s) of xso that (3)0x xx−=. Note: In this example we could cancel out the x’s to get just (3)x−, but we still have the restriction: 0x≠. This will be discussed in detail in sections 1.5 and 4.5.
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