Multiply $ \dfrac{1}{4} $ by $ x^2+4x+4 $ to get $ \dfrac{ x^2+4x+4 }{ 4 } $.

Step 1: Write $ x^2+4x+4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{4} \cdot x^2+4x+4 & \xlongequal{\text{Step 1}} \frac{1}{4} \cdot \frac{x^2+4x+4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( x^2+4x+4 \right) }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2+4x+4 }{ 4 } \end{aligned} $$

Add $ \dfrac{-x^2-4x-4}{4} $ and $ 3 $ to get $ \dfrac{ \color{purple}{ -x^2-4x+8 } }{ 4 }$.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{4}$.

$$ \begin{aligned} \frac{-x^2-4x-4}{4} +3 & \xlongequal{\text{Step 1}} \frac{-x^2-4x-4}{4} + \frac{3}{\color{red}{1}} = \frac{ -x^2-4x-4 }{ 4 } + \frac{ 3 \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -x^2-4x-4 } }{ 4 } + \frac{ \color{purple}{ 12 } }{ 4 }=\frac{ \color{purple}{ -x^2-4x+8 } }{ 4 } \end{aligned} $$