Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $.

Subtract $ \dfrac{1}{6} $ from $ x^2 $ to get $ \dfrac{ \color{purple}{ 6x^2-1 } }{ 6 }$.

Step 1: Write $ x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 6 }$.

$$ \begin{aligned} x^2- \frac{1}{6} & \xlongequal{\text{Step 1}} \frac{x^2}{\color{red}{1}} - \frac{1}{6} = \frac{ x^2 \cdot \color{blue}{ 6 }}{ 1 \cdot \color{blue}{ 6 }} - \frac{ 1 }{ 6 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 6x^2 } }{ 6 } - \frac{ \color{purple}{ 1 } }{ 6 }=\frac{ \color{purple}{ 6x^2-1 } }{ 6 } \end{aligned} $$

Add $ \dfrac{6x^2-1}{6} $ and $ \dfrac{x}{6} $ to get $ \dfrac{6x^2+x-1}{6} $.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{6x^2-1}{6} + \frac{x}{6} & = \frac{6x^2-1}{\color{blue}{6}} + \frac{x}{\color{blue}{6}} =\frac{ 6x^2-1 + x }{ \color{blue}{ 6 }} = \\[1ex] &= \frac{6x^2+x-1}{6} \end{aligned} $$