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

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.

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

Subtract $ \dfrac{1}{x} $ from $ \dfrac{3x}{4} $ to get $ \dfrac{ \color{purple}{ 3x^2-4 } }{ 4x }$.

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}{ x }$ and the second by $\color{blue}{ 4 }$.

$$ \begin{aligned} \frac{3x}{4} - \frac{1}{x} & = \frac{ 3x \cdot \color{blue}{ x }}{ 4 \cdot \color{blue}{ x }} - \frac{ 1 \cdot \color{blue}{ 4 }}{ x \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ 3x^2 } }{ 4x } - \frac{ \color{purple}{ 4 } }{ 4x }=\frac{ \color{purple}{ 3x^2-4 } }{ 4x } \end{aligned} $$

Subtract $3$ from $ \dfrac{3x^2-4}{4x} $ to get $ \dfrac{ \color{purple}{ 3x^2-12x-4 } }{ 4x }$.

Step 1: Write $ 3 $ 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 second fraction by $\color{blue}{4x}$.

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