Functions Modeling Change: A Preparation for Calculus, 5th Edition

$$x=\frac{3+\sqrt{17}}{4},\:x=\frac{3-\sqrt{17}}{4}$$
Using the rules of algebra, we obtain: $$2x-3=\frac{\left(2x-1\right)}{2x+1} \\ 2x\left(2x+1\right)-3\left(2x+1\right)=\frac{2x-1}{2x+1}\left(2x+1\right) \\ x=\frac{3+\sqrt{17}}{4},\:x=\frac{3-\sqrt{17}}{4}$$