Answer
$\frac{4}{3}(1-x)\sqrt (4x-1)$
Work Step by Step
$(4x-1)^{1/2}-\frac{1}{3}(4x-1)^{3/2}$
The greatest common factor of $(4x-1)^{1/2}-\frac{1}{3}(4x-1)^{3/2}$ is $(4x-1)$ with the smaller exponent in the two terms. Thus the greatest common factor is $(4x-1)^{1/2}$
Express each term as the product of greatest common factor and its other factor.
$=(4x-1)^{1/2}-\frac{1}{3}(4x-1)(4x-1)^{1/2}$
$[(4x-1)^{1}(4x-1)^{1/2}=(4x-1)^{1+1/2} =(4x-1)^{3/2}]$
Factor out the Greatest common factor.
$=(4x-1)^{1/2}(1-\frac{1}{3}(4x-1))$
Simplify
$=(4x-1)^{1/2}[\frac{(3-(4x-1))}{3}]$
$=(4x-1)^{1/2}[\frac{(3-4x+1)}{3}]$
$=(4x-1)^{1/2}[\frac{(4-4x)}{3}]$
Take out common factor 4 from $(4-4x)$
$=(4x-1)^{1/2}[\frac{4(1-x)}{3}]$
$=(4x-1)^{1/2}(\frac{4}{3})(1-x)$
$=(\frac{4}{3})(1-x)(4x-1)^{1/2}$
$=(\frac{4}{3})(1-x)\sqrt (4x-1)$
