Remove 1 from denominator.

Multiply $ \dfrac{1}{4} $ by $ \dfrac{x}{3} $ to get $ \dfrac{ x }{ 12 } $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{4} \cdot \frac{x}{3} \xlongequal{\text{Step 1}} \frac{ 1 \cdot x }{ 4 \cdot 3 } \xlongequal{\text{Step 2}} \frac{ x }{ 12 } \end{aligned} $$

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

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{7}{2} \cdot x & \xlongequal{\text{Step 1}} \frac{7}{2} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7 \cdot x }{ 2 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 7x }{ 2 } \end{aligned} $$

Subtract $ \dfrac{x}{12} $ from $ 1 $ to get $ \dfrac{ \color{purple}{ -x+12 } }{ 12 }$.

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

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

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

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{7}{2} \cdot x & \xlongequal{\text{Step 1}} \frac{7}{2} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7 \cdot x }{ 2 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 7x }{ 2 } \end{aligned} $$

Add $ \dfrac{-x+12}{12} $ and $ \dfrac{7x}{2} $ to get $ \dfrac{ \color{purple}{ 41x+12 } }{ 12 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{6}$.

$$ \begin{aligned} \frac{-x+12}{12} + \frac{7x}{2} & = \frac{ -x+12 }{ 12 } + \frac{ 7x \cdot \color{blue}{ 6 }}{ 2 \cdot \color{blue}{ 6 }} = \\[1ex] &=\frac{ \color{purple}{ -x+12 } }{ 12 } + \frac{ \color{purple}{ 42x } }{ 12 }=\frac{ \color{purple}{ 41x+12 } }{ 12 } \end{aligned} $$