Multiply $ \dfrac{5}{12} $ by $ x^2 $ to get $ \dfrac{ 5x^2 }{ 12 } $.

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.

$$ \begin{aligned} \frac{5}{12} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{5}{12} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x^2 }{ 12 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2 }{ 12 } \end{aligned} $$

Add $ \dfrac{5x^2}{12} $ and $ 23x $ to get $ \dfrac{ \color{purple}{ 5x^2+276x } }{ 12 }$.

Step 1: Write $ 23x $ 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 $\color{blue}{12}$.

$$ \begin{aligned} \frac{5x^2}{12} +23x & \xlongequal{\text{Step 1}} \frac{5x^2}{12} + \frac{23x}{\color{red}{1}} = \frac{ 5x^2 }{ 12 } + \frac{ 23x \cdot \color{blue}{ 12 }}{ 1 \cdot \color{blue}{ 12 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5x^2 } }{ 12 } + \frac{ \color{purple}{ 276x } }{ 12 }=\frac{ \color{purple}{ 5x^2+276x } }{ 12 } \end{aligned} $$

Add $ \dfrac{5x^2+276x}{12} $ and $ 10 $ to get $ \dfrac{ \color{purple}{ 5x^2+276x+120 } }{ 12 }$.

Step 1: Write $ 10 $ 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 $\color{blue}{12}$.

$$ \begin{aligned} \frac{5x^2+276x}{12} +10 & \xlongequal{\text{Step 1}} \frac{5x^2+276x}{12} + \frac{10}{\color{red}{1}} = \frac{ 5x^2+276x }{ 12 } + \frac{ 10 \cdot \color{blue}{ 12 }}{ 1 \cdot \color{blue}{ 12 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5x^2+276x } }{ 12 } + \frac{ \color{purple}{ 120 } }{ 12 }=\frac{ \color{purple}{ 5x^2+276x+120 } }{ 12 } \end{aligned} $$