Examples of algebraic fractions are $$\frac{\Tred{x}^2-\Tred{x}+1}{\Tred{x}+3},\quad\frac{1}{\sqrt{\Tred{y}} - 1}$$
The algebraic fraction $\displaystyle\frac{\Tred{x}-1}{\Tred{x}^2+1}$ evaluated when $\Tred{x} = 5$ is equal to $$\frac{\Tred{5}-1}{\Tred{5}^2+1} = \frac{4}{26} = \frac{2}{13}.$$