Science:Math Exam Resources/Courses/MATH100/December 2016/Question 02 (b)/Solution 1

By the quotient rule,

${\begin{aligned}g'(x)&={\frac {(2x)(2x-1)-(x^{2}+3)(2)}{(2x-1)^{2}}}\\&={\frac {4x^{2}-2x-2x^{2}-6}{(2x-1)^{2}}}\\&={\color {blue}{\frac {2(x^{2}-x-3)}{(2x-1)^{2}}}}.\\\end{aligned}}$