Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00 Edition
ISBN: 9780395977224
Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher: McDougal Littell
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Question
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Chapter 10, Problem 16MS
To determine

To solve: the equation if it is an identity or has no solution.

Expert Solution & Answer
Check Mark

Answer to Problem 16MS

Equation has a solution.

Explanation of Solution

Given information:

  3xx+1−1x=x+1x

Formula used:

Step 1. Check where the denominator is zero.

Step 2. Taking L.C.M.

Step 3. Multiply with the L.C.M on both the sides.

Step 4. Solve the following equation.

Calculation:

Consider,

  3xx+1−1x=x+1x

Now, x≠0 and x≠−1.

  =(x)(x+1)[3xx+1−1x]=(x)(x+1)[x+1x]=(x)(3x)−(x+1)=(x+1)(x+1)=3x2−x−1=(x+1)2=3x2−x−1−x2−2x−1=0=2x2−3x−2=0

Further solving using middle term

  =2x2−3x−2=0=2x2−4x+x−2=0=2x(x−2)+1(x−2)=0=(2x+1)(x−2)=0

  =(2x+1)=0=2x=−1=x=−12 or =(x−2)=0=x=2

Putting value of x in equation

  =x=2=3(2)(2)+1−1(2)=(2)+1(2)=63−12=32=12−36=32=(96)=32=32=32

Hence, L.H.S=R.H.S

Therefore, the solution set is {2,−12} .

Previous
Chapter 10, Problem 15MS
Next
Chapter 10, Problem 17MS

Chapter 10 Solutions

Algebra: Structure And Method, Book 1

Ch. 10.1 - Prob. 1OECh. 10.1 - Prob. 2OECh. 10.1 - Prob. 3OECh. 10.1 - Prob. 4OECh. 10.1 - Prob. 5OECh. 10.1 - Prob. 6OECh. 10.1 - Prob. 7OECh. 10.1 - Prob. 8OECh. 10.1 - Prob. 9OECh. 10.1 - Prob. 10OE
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Prob. 6MRECh. 10.5 - Prob. 7MRECh. 10.5 - Prob. 8MRECh. 10.5 - Prob. 9MRECh. 10.5 - Prob. 10MRECh. 10.6 - Prob. 1OECh. 10.6 - Prob. 2OECh. 10.6 - Prob. 3OECh. 10.6 - Prob. 4OECh. 10.6 - Prob. 5OECh. 10.6 - Prob. 6OECh. 10.6 - Prob. 7OECh. 10.6 - Prob. 8OECh. 10.6 - Prob. 1WECh. 10.6 - Prob. 2WECh. 10.6 - Prob. 3WECh. 10.6 - Prob. 4WECh. 10.6 - Prob. 5WECh. 10.6 - Prob. 6WECh. 10.6 - Prob. 7WECh. 10.6 - Prob. 8WECh. 10.6 - Prob. 9WECh. 10.6 - Prob. 10WECh. 10.6 - Prob. 11WECh. 10.6 - Prob. 12WECh. 10.6 - Prob. 13WECh. 10.6 - Prob. 14WECh. 10.6 - Prob. 15WECh. 10.6 - Prob. 16WECh. 10.6 - Prob. 17WECh. 10.6 - Prob. 18WECh. 10.6 - Prob. 19WECh. 10.6 - Prob. 20WECh. 10.6 - Prob. 21WECh. 10.6 - Prob. 22WECh. 10.6 - Prob. 23WECh. 10.6 - Prob. 24WECh. 10.6 - Prob. 25WECh. 10.6 - Prob. 1MRECh. 10.6 - Prob. 2MRECh. 10.6 - Prob. 3MRECh. 10.6 - Prob. 4MRECh. 10.6 - Prob. 5MRECh. 10.6 - Prob. 6MRECh. 10.6 - Prob. 7MRECh. 10.6 - Prob. 8MRECh. 10.6 - Prob. 9MRECh. 10.6 - Prob. 10MRECh. 10.6 - Prob. 11MRECh. 10.6 - 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Introduction to Algebra: Using Variables; Author: Professor Dave Explains;https://www.youtube.com/watch?v=WZdZhuUSmpM;License: Standard YouTube License, CC-BY