Solve the following using BOTH METHODS from the attached examples, which you show clearly. Then discuss which one is preferable: (3x^-1 + y^-1) / (9x^-2 - y^-2) =

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Solve the following using BOTH METHODS from the attached examples, which you show clearly.  Then discuss which one is preferable:

(3x^-1 + y^-1)  /  (9x^-2 - y^-2) = 

Example 1 How to Simplify a Complex Rational Expression Using Method I
Simplify:
Step-by-Step Solution
x+3
Notice that x cannot equal –3 because that would make the denominator, , equal zero; x cannot equal O because it would make the
expression in the numerator undefined.
Step 1:Write the numerator of the complex rational expression as a single rational expression.
The least common denominator of - and is 3x.
1
3. +
3x
a+b
:
x+3
Step 2:Write the denominator of the complex This is already done. rational expression as a single rational expression.
Step 3Rewrite the complex rational expression using the rational expressions found in Steps 1 and 2.
x+3
3x
e+3
x+3
Step 4Simplify the rational expression using the techniques for dividing rational expressions from Section 5.1 D.
x+3
3x
2
Multiply the numerator by the reciprocal of the denominator:
r+3
(a+3) -2
3z (3)
Multiply; divide out common factors:
-
||||
Transcribed Image Text:Example 1 How to Simplify a Complex Rational Expression Using Method I Simplify: Step-by-Step Solution x+3 Notice that x cannot equal –3 because that would make the denominator, , equal zero; x cannot equal O because it would make the expression in the numerator undefined. Step 1:Write the numerator of the complex rational expression as a single rational expression. The least common denominator of - and is 3x. 1 3. + 3x a+b : x+3 Step 2:Write the denominator of the complex This is already done. rational expression as a single rational expression. Step 3Rewrite the complex rational expression using the rational expressions found in Steps 1 and 2. x+3 3x e+3 x+3 Step 4Simplify the rational expression using the techniques for dividing rational expressions from Section 5.1 D. x+3 3x 2 Multiply the numerator by the reciprocal of the denominator: r+3 (a+3) -2 3z (3) Multiply; divide out common factors: - ||||
Example 3 How to Simplify a Complex Rational Expression Using Method II
Simplify:
Step-by-Step Solution
Step 1Find the least common denominator of all the denominators in the complex rational expression.
The denominators of the complex rational expression are 3, x, and 2. The least common denominator is 2·3· x = 6x.
Step 2Multiply both the numerator and the denominator of the complex rational expression by the LCD found in Step 1.
(프)·6z
Distribute 6x to each term:
Step 3Simplify the rational expression.
2x+6
Simplify:
3z(x+3)
2 (+3)
3z (+3)
Factor and divide out common factors:
2
3x
Transcribed Image Text:Example 3 How to Simplify a Complex Rational Expression Using Method II Simplify: Step-by-Step Solution Step 1Find the least common denominator of all the denominators in the complex rational expression. The denominators of the complex rational expression are 3, x, and 2. The least common denominator is 2·3· x = 6x. Step 2Multiply both the numerator and the denominator of the complex rational expression by the LCD found in Step 1. (프)·6z Distribute 6x to each term: Step 3Simplify the rational expression. 2x+6 Simplify: 3z(x+3) 2 (+3) 3z (+3) Factor and divide out common factors: 2 3x
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