Precalc0006to0010-page32

Precalc0006to0010-page32 - subtract 1 from the numerator....

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(Section 0.10: More Algebraic Manipulations) 0.10.3 PART D: COMPENSATION Sometimes, we can alter an expression if we compensate for the change and maintain equivalence. Example 3 (Compensation Using Addition and Subtraction) Fill in the box below with an appropriate, simplified expression: x x + 1 = 1 ± § Solution We know that x + 1 x + 1 = 1 x ±² 1 () , so we would like to add 1 to the numerator of x x + 1 . To compensate for that, we must also
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Unformatted text preview: subtract 1 from the numerator. WARNING 3 : If we add 1 to the numerator of a fraction, we cannot compensate by adding 1 to the denominator. For example, 1 2 2 3 . x x + 1 = x + 1 1 x + 1 = x + 1 x + 1 1 x + 1 = 1 1 x + 1 Answer: x x + 1 = 1 1 x + 1 A similar compensation technique is used when Completing the Square (CTS) in Sections 0.11, 0.13, and 2.2 and Chapter 10....
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This document was uploaded on 12/29/2011.

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