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 19MS
To determine

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

Expert Solution & Answer
Check Mark

Answer to Problem 19MS

Equation has a solution.

Explanation of Solution

Given information:

  x2+12x2−4−1x−2=3x−2

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,

  x2+12x2−4−1x−2=3x−2

Re-writing the equation we have,

  x2+12(x−2)(x+2)−1x−2=3x−2

Now, x≠2 and x≠−2.

  =(x−2)(x+2)[x2+12(x−2)(x+2)−1x−2]=(x−2)(x+2)[3x−2]=x2+12−(x+2)(1)=3(x+2)=x2+12−x−2=3x+6=x2+10−x−3x−6=0=x2−4x+4=0

Further, solving we get,

   = (x−2) 2 =0=(x−2)(x−2)=0=(x−2)=0         or           (x−2)=0=x=2                 or              x=2

Putting value of x in equation

  =x=2=(2)2+12(2)2−4−12−2=32−2=0=0

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

Therefore, the solution set is {2} .

Previous
Chapter 10, Problem 18MS
Next
Chapter 10, Problem 20MS

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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Publisher:McGraw-Hill Education
SEE MORE TEXTBOOKS
Introduction to Algebra: Using Variables; Author: Professor Dave Explains;https://www.youtube.com/watch?v=WZdZhuUSmpM;License: Standard YouTube License, CC-BY