Vx + 2 Rationalize the numerator:

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
Section: Chapter Questions
Problem 49E
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EXAMPLE 7
Vx - 3
Rationalize the numerator:
Strategy
To rationalize the numerator, we will multiply the numerator and the denominator by the conjugate of the numerator.
Why
After rationalizing the numerator, we can simplify the expression. Although the result will not be in simplified form, this non-simplified form is often desirable in calculus.
Solution
We multiply the numerator and denominator by Vx + 3, which is the conjugate of the numerator.
3
Vx - 3
Vx + 3
Multiply by a form of 1 to rationalize the numerator.
Vx + 3
(Vx)? - (3)2
Multiply the numerators using a special-product rule.
Multiply the denominators.
x +
Vx
x + 3/x
The final expression is not in simplified form. However, this non-simplified form is often desirable in calculus.
Self Check 7
Vx + 2
Rationalize the numerator:
Transcribed Image Text:EXAMPLE 7 Vx - 3 Rationalize the numerator: Strategy To rationalize the numerator, we will multiply the numerator and the denominator by the conjugate of the numerator. Why After rationalizing the numerator, we can simplify the expression. Although the result will not be in simplified form, this non-simplified form is often desirable in calculus. Solution We multiply the numerator and denominator by Vx + 3, which is the conjugate of the numerator. 3 Vx - 3 Vx + 3 Multiply by a form of 1 to rationalize the numerator. Vx + 3 (Vx)? - (3)2 Multiply the numerators using a special-product rule. Multiply the denominators. x + Vx x + 3/x The final expression is not in simplified form. However, this non-simplified form is often desirable in calculus. Self Check 7 Vx + 2 Rationalize the numerator:
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