\frac{x^2 + 1}{2x^2 + 3 } = \frac{ x^2 + \frac{3}{2} - \frac{1}{2}}{2x^2 + 3 } = \frac{\frac{1}{2}(2x^2 + 3 ) - \frac{1}{2}}{2x^2 + 3 } = \frac{1}{2} - \frac{1}{4x^2 + 6 }