Factoring Algebraic Expressions with Fractional Exponents

[DecayProduct]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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

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

What am I missing?

 

[Cyosis]

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.

 

[berkeman]

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?

 

[DecayProduct]

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!