Factoring Algebraic Expressions with Fractional Exponents

Click For Summary

Homework Help Overview

The discussion revolves around factoring an algebraic expression involving fractional exponents, specifically the expression (4x-1)^{1/2}-1/3(4x-1)^{3/2}. Participants are examining the steps taken to factor the expression and comparing their results with a provided answer from a textbook.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to factor the expression by identifying the greatest common factor (GCF) and expresses confusion over discrepancies between their result and the textbook answer. Some participants question the validity of the textbook answer, while others suggest verifying the results by substituting specific values for x.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and checking assumptions about the correctness of the textbook answer. There is no explicit consensus, but some guidance has been offered regarding verification through numerical substitution.

Contextual Notes

Participants are navigating potential errors in their calculations and the accuracy of the textbook solution. The original poster expresses uncertainty about their results and seeks confirmation from others.

DecayProduct
Messages
67
Reaction score
0

Homework Statement



[tex](4x-1)^{1/2}-1/3(4x-1)^{3/2}[/tex]

Homework Equations


The Attempt at a Solution



I think the GCF is [tex](4x-1)^{1/2}[/tex]. So, I get [tex](4x-1)^{1/2}(1+(-1/3(4x-1)))[/tex] = [tex](4x-1)^{1/2}(-4/3x+4/3)[/tex] = [tex]-4/3(4x-1)^{1/2}(x-1)[/tex]

However, the answer in the book is [tex]4/3(4x-1)^{1/2}(x-1)[/tex]. I've done it several ways, and I either get a minus sign on the [tex]4/3[/tex], or the [tex](x-1)[/tex] becomes [tex](x+1)[/tex].

What am I missing?
 
Physics news on Phys.org
If the problem you've listed is the same as the problem in your book, then you're right and the answer in your book is wrong.
 
Last edited:
You can also check your work versus the book answer by plugging in a number for x, and solving the original expression and your final expression with a calculator. What answers do you get, for example, for x = 2?
 
Thanks folks! I did try inputting a value for x, but I was still put off by the book's answer. I just wanted to verify from those more knowledgeable than I.

Thanks!
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
4
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
8
Views
2K
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
2
Views
2K