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

By the quotient rule,

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