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 ISimplify:Step-by-Step Solutionx+3Notice that x cannot equal –3 because that would make the denominator, , equal zero; x cannot equal O because it would make theexpression 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.13. +3xa+b:x+3Step 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+33xe+3x+3Step 4Simplify the rational expression using the techniques for dividing rational expressions from Section 5.1 D.x+33x2Multiply the numerator by the reciprocal of the denominator:r+3(a+3) -23z (3)Multiply; divide out common factors:-|||| Example 3 How to Simplify a Complex Rational Expression Using Method IISimplify:Step-by-Step SolutionStep 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)·6zDistribute 6x to each term:Step 3Simplify the rational expression.2x+6Simplify:3z(x+3)2 (+3)3z (+3)Factor and divide out common factors:23x

Given , 3x-1+y-19x-2-y-2=3x+1y9x2-1y2 We have to simplify the given problem by two methods showed in…

Answered: Solve the following using BOTH METHODS…

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) =

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 48E

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Question

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:
-
||||

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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