Subtract $ \dfrac{1}{9} $ from $ x^2 $ to get $ \dfrac{ \color{purple}{ 9x^2-1 } }{ 9 }$.

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 $\color{blue}{ 9 }$.

$$ \begin{aligned} x^2- \frac{1}{9} & \xlongequal{\text{Step 1}} \frac{x^2}{\color{red}{1}} - \frac{1}{9} = \frac{ x^2 \cdot \color{blue}{ 9 }}{ 1 \cdot \color{blue}{ 9 }} - \frac{ 1 }{ 9 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9x^2 } }{ 9 } - \frac{ \color{purple}{ 1 } }{ 9 }=\frac{ \color{purple}{ 9x^2-1 } }{ 9 } \end{aligned} $$