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Factoring Algebraic Expressions with Fractional Exponents

  • #1

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?
 

Answers and Replies

  • #2
Cyosis
Homework Helper
1,495
0
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:
  • #3
berkeman
Mentor
56,661
6,559
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?
 
  • #4
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!
 

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