Precalc0006to0010-page26

# Precalc0006to0010-page26 - but possibly introduce them in...

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(Section 0.9: Simplifying Algebraic Expressions) 0.9.8 PART E: RATIONALIZING DENOMINATORS AND NUMERATORS When we rationalize the denominator of a fraction, we eliminate radicals and non-integer exponents in the denominator but possibly introduce them in the numerator. For example, 1 2 is unacceptable in a simplified expression, so we rewrite it: 1 2 = 1 2 ± 2 2 = 2 2 . For more complicated expressions, there are different opinions as to when denominators need to be rationalized. (See Footnote 1) When we rationalize the numerator of a fraction, we eliminate radicals and non-integer exponents in the numerator
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Unformatted text preview: but possibly introduce them in the denominator. Example 3 (Rationalizing a Numerator) Re-express x + h ± x h by rationalizing the numerator. • This expression is an example of a difference quotient (see Section 1.10). Rationalizing the numerator will help us find a derivative (see Section 1.11). § Solution We will multiply the numerator and the denominator by x + h + x , the conjugate of x + h ± x . x + h ± x h = x + h ± x ( ) h ² x + h + x ( ) x + h + x ( ) To multiply out the numerator, we use the rule: a ± b ( ) a + b ( ) = a 2 ± b 2 ....
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