Multiply $ \dfrac{49}{4} $ by $ x^2 $ to get $ \dfrac{ 49x^2 }{ 4 } $.

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.

$$ \begin{aligned} \frac{49}{4} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{49}{4} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 49 \cdot x^2 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 49x^2 }{ 4 } \end{aligned} $$

Subtract $ \dfrac{49x^2}{4} $ from $ x^2 $ to get $ \dfrac{ \color{purple}{ -45x^2 } }{ 4 }$.

Step 1: Write $ x^2 $ 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 $\color{blue}{ 4 }$.

$$ \begin{aligned} x^2- \frac{49x^2}{4} & \xlongequal{\text{Step 1}} \frac{x^2}{\color{red}{1}} - \frac{49x^2}{4} = \frac{ x^2 \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} - \frac{ 49x^2 }{ 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4x^2 } }{ 4 } - \frac{ \color{purple}{ 49x^2 } }{ 4 }=\frac{ \color{purple}{ -45x^2 } }{ 4 } \end{aligned} $$

Add $ \dfrac{-45x^2}{4} $ and $ 24x $ to get $ \dfrac{ \color{purple}{ -45x^2+96x } }{ 4 }$.

Step 1: Write $ 24x $ 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 $\color{blue}{4}$.

$$ \begin{aligned} \frac{-45x^2}{4} +24x & \xlongequal{\text{Step 1}} \frac{-45x^2}{4} + \frac{24x}{\color{red}{1}} = \frac{ -45x^2 }{ 4 } + \frac{ 24x \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -45x^2 } }{ 4 } + \frac{ \color{purple}{ 96x } }{ 4 }=\frac{ \color{purple}{ -45x^2+96x } }{ 4 } \end{aligned} $$