# Factoring problem with negative and rational exponents

• September 1st 2010, 05:08 PM
jorygoldsmith
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
• September 1st 2010, 05:15 PM
jorygoldsmith
x^(-1/2)(3x+4)^(1/2)+3x^(1/2)(3x+4)^(-1/2)

should be written like this sorry
• September 1st 2010, 05:30 PM
skeeter
Quote:

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

should be written like this sorry

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

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

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

$\displaystyle \frac{2(3x+2)}{\sqrt{x(3x+4)}}$
• September 1st 2010, 05:33 PM
jorygoldsmith
$\displaystyle \frac{1}{h} \left[\frac{1}{(x+h)^2} - \frac{1}{x^2}\right]$