Answer
$\frac{6 (2+x)}{x^{3/4}}$
Work Step by Step
$12x^{-3/4} + 6x^{1/4}$
Take out common factor,
$= 6(2x^{-3/4} + x^{1/4})$
The greatest common factor is $x$ with the smaller exponent in the two terms. Thus the greatest common factor is $(x)^{-3/4}$
Express each term as the product of greatest common factor and its other factor.
$= 6(2x^{-3/4} + x^{-3/4}. x)$ $[ x^{-3/4}. x = x^{-3/4 + 1} = x^{1/4}]$
Factor out the Greatest common factor.
$= 6(x^{-3/4})(2+x)$
$= 6(2+x)(x^{-3/4})$
$=\frac{6(2+x)}{(x^{3/4})}$ $[a^{-1/m} = \frac{1}{a^{1/m}}]$
