Answer
$\dfrac{(4x^{2}+1)(36x^{2}-16x+1)}{(2x-1)^{1/2}}$
Work Step by Step
$(4x^{2}+1)^{2}(2x-1)^{-1/2}+16x(4x^{2}+1)(2x-1)^{1/2}$
Take out common factor $(4x^{2}-1)(2x-1)^{-1/2}$ from the expression:
$(4x^{2}+1)^{2}(2x-1)^{-1/2}+16x(4x^{2}+1)(2x-1)^{1/2}=...$
$...=(4x^{2}+1)(2x-1)^{-1/2}[(4x^{2}+1)+16x(2x-1)]=...$
Simplify the expression inside brackets:
$...=(4x^{2}+1)(2x-1)^{-1/2}(4x^{2}+1+32x^{2}-16x)=...$
$...=(4x^{2}+1)(2x-1)^{-1/2}(36x^{2}-16x+1)=...$
Change the sign of the exponent of $2x-1$ by putting the factor as a denominator:
$...=\dfrac{(4x^{2}+1)(36x^{2}-16x+1)}{(2x-1)^{1/2}}$
