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!