Subtract $ \dfrac{a}{9a+2} $ from $ 7a+4 $ to get $ \dfrac{ \color{purple}{ 63a^2+49a+8 } }{ 9a+2 }$.

Step 1: Write $ 7a+4 $ 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 $\color{blue}{ 9a+2 }$.

$$ \begin{aligned} 7a+4- \frac{a}{9a+2} & \xlongequal{\text{Step 1}} \frac{7a+4}{\color{red}{1}} - \frac{a}{9a+2} = \frac{ \left( 7a+4 \right) \cdot \color{blue}{ \left( 9a+2 \right) }}{ 1 \cdot \color{blue}{ \left( 9a+2 \right) }} - \frac{ a }{ 9a+2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 63a^2+14a+36a+8 } }{ 9a+2 } - \frac{ \color{purple}{ a } }{ 9a+2 }=\frac{ \color{purple}{ 63a^2+49a+8 } }{ 9a+2 } \end{aligned} $$