Subtract $ \dfrac{2x-1}{6x+18} $ from $ \dfrac{x+1}{4x+12} $ to get $ \dfrac{ \color{purple}{ -x+5 } }{ 12x+36 }$.

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}{ 3 }$ and the second by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{x+1}{4x+12} - \frac{2x-1}{6x+18} & = \frac{ \left( x+1 \right) \cdot \color{blue}{ 3 }}{ \left( 4x+12 \right) \cdot \color{blue}{ 3 }} - \frac{ \left( 2x-1 \right) \cdot \color{blue}{ 2 }}{ \left( 6x+18 \right) \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 3x+3 } }{ 12x+36 } - \frac{ \color{purple}{ 4x-2 } }{ 12x+36 }=\frac{ \color{purple}{ 3x+3 - \left( 4x-2 \right) } }{ 12x+36 } = \\[1ex] &=\frac{ \color{purple}{ -x+5 } }{ 12x+36 } \end{aligned} $$