Math Help - Factoring problem with negative and rational exponents

1. Factoring problem with negative and rational exponents

I just can't seem to get this one, it's in the first assignment of my semester...

Factor:
x^-1/2(3x+4)^1/2+3x^1/2(3x+4)^-1/2

thanks for any hel;p, i just want to know how to do it not even the answer necessarily

2. x^(-1/2)(3x+4)^(1/2)+3x^(1/2)(3x+4)^(-1/2)

should be written like this sorry

3. Originally Posted by jorygoldsmith
x^(-1/2)(3x+4)^(1/2)+3x^(1/2)(3x+4)^(-1/2)

should be written like this sorry
$x^{-1/2}(3x+4)^{1/2} + 3x^{1/2}(3x+4)^{-1/2}$

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

$[x(3x+4)]^{-1/2}(6x+4)$

$\displaystyle \frac{2(3x+2)}{\sqrt{x(3x+4)}}$

[(x+h)^(-2)-(x)^(-2)]/h

5. easier this way ...

$\displaystyle \frac{1}{h} \left[\frac{1}{(x+h)^2} - \frac{1}{x^2}\right]$

get a common denominator and combine the two fractions inside the [brackets], then combine like terms and factor the numerator ... ultimate goal is to get the "h" in the first fraction to cancel.

also ... next time, start a new problem w/ a new thread.