Multiply $ \dfrac{4}{7} $ by $ x^2 $ to get $ \dfrac{ 4x^2 }{ 7 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{4}{7} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{4}{7} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4 \cdot x^2 }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^2 }{ 7 } \end{aligned} $$

Add $x$ and $ \dfrac{4x^2}{7} $ to get $ \dfrac{ \color{purple}{ 4x^2+7x } }{ 7 }$.

Step 1: Write $ x $ 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 first fraction by $\color{blue}{ 7 }$.

$$ \begin{aligned} x+ \frac{4x^2}{7} & \xlongequal{\text{Step 1}} \frac{x}{\color{red}{1}} + \frac{4x^2}{7} = \frac{ x \cdot \color{blue}{ 7 }}{ 1 \cdot \color{blue}{ 7 }} + \frac{ 4x^2 }{ 7 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7x } }{ 7 } + \frac{ \color{purple}{ 4x^2 } }{ 7 }=\frac{ \color{purple}{ 4x^2+7x } }{ 7 } \end{aligned} $$

Add $ \dfrac{4x^2+7x}{7} $ and $ 28x $ to get $ \dfrac{ \color{purple}{ 4x^2+203x } }{ 7 }$.

Step 1: Write $ 28x $ 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 $\color{blue}{7}$.

$$ \begin{aligned} \frac{4x^2+7x}{7} +28x & \xlongequal{\text{Step 1}} \frac{4x^2+7x}{7} + \frac{28x}{\color{red}{1}} = \frac{ 4x^2+7x }{ 7 } + \frac{ 28x \cdot \color{blue}{ 7 }}{ 1 \cdot \color{blue}{ 7 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4x^2+7x } }{ 7 } + \frac{ \color{purple}{ 196x } }{ 7 }=\frac{ \color{purple}{ 4x^2+203x } }{ 7 } \end{aligned} $$