I'm having trouble with this problem.

The only way I can get the answer the book gives is to illegally remove the exponent of 1/2 from the 1st term.

Problem: (2x+1)^(1/2) + (x+3)(2x+1)^(-1/2)

my attempt:

=(2x+1)^(1/2) + ((x+3) / ((2x + 1)^(1/2))

(I don't see any like terms here unless I remove the exponent)

Book's answer: (3x+4) / (sqrt(2x+1))

Another question: I see that I should move (2x+1)^(-1/2) to the denominator because of the negative exponent. When I do this, does it go in the denominator of all the other terms, or just in the den of (x+3)?

Please explain what I'm doing wrong. Thanks alot!!

I expect you've been asked to simplify this... To simplify expressions involving fractions, you need a common denominator.

\(\displaystyle \sqrt{2x + 1} + \frac{x + 3}{\sqrt{2x + 1}} = \frac{\sqrt{2x + 1}\sqrt{2x + 1}}{\sqrt{2x + 1}} + \frac{x + 3}{\sqrt{2x + 1}}\)

\(\displaystyle = \frac{2x + 1}{\sqrt{2x + 1}} + \frac{x + 3}{\sqrt{2x + 1}}\)

\(\displaystyle = \frac{2x + 1 + x + 3}{\sqrt{2x + 1}}\)

\(\displaystyle = \frac{3x + 4}{\sqrt{2x + 1}}\).

I choose to write fractions with rational denominators though, so to clean it up even more...

\(\displaystyle = \frac{(3x + 4)\sqrt{2x + 1}}{2x + 1}\).