# Factoring Algebraic Expressions with Fractional Exponents

1. May 21, 2009

### DecayProduct

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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?

2. May 21, 2009

### 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.

Last edited: May 21, 2009
3. May 21, 2009

### Staff: Mentor

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. May 21, 2009

### 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!

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