Subtract $ \dfrac{p}{9p+2} $ from $ 6p+10 $ to get $ \dfrac{ \color{purple}{ 54p^2+101p+20 } }{ 9p+2 }$.

Step 1: Write $ 6p+10 $ 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 $\color{blue}{ 9p+2 }$.

$$ \begin{aligned} 6p+10- \frac{p}{9p+2} & \xlongequal{\text{Step 1}} \frac{6p+10}{\color{red}{1}} - \frac{p}{9p+2} = \frac{ \left( 6p+10 \right) \cdot \color{blue}{ \left( 9p+2 \right) }}{ 1 \cdot \color{blue}{ \left( 9p+2 \right) }} - \frac{ p }{ 9p+2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 54p^2+12p+90p+20 } }{ 9p+2 } - \frac{ \color{purple}{ p } }{ 9p+2 }=\frac{ \color{purple}{ 54p^2+101p+20 } }{ 9p+2 } \end{aligned} $$