Subtract $ \dfrac{1}{18} $ from $ \dfrac{x}{16} $ to get $ \dfrac{ \color{purple}{ 9x-8 } }{ 144 }$.

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}{ 9 }$ and the second by $\color{blue}{ 8 }$.

$$ \begin{aligned} \frac{x}{16} - \frac{1}{18} & = \frac{ x \cdot \color{blue}{ 9 }}{ 16 \cdot \color{blue}{ 9 }} - \frac{ 1 \cdot \color{blue}{ 8 }}{ 18 \cdot \color{blue}{ 8 }} = \\[1ex] &=\frac{ \color{purple}{ 9x } }{ 144 } - \frac{ \color{purple}{ 8 } }{ 144 }=\frac{ \color{purple}{ 9x-8 } }{ 144 } \end{aligned} $$

Add $ \dfrac{1}{9} $ and $ \dfrac{1}{12} $ to get $ \dfrac{ \color{purple}{ 7 } }{ 36 }$.

To add fractions they must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 4 }$ and the second by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{1}{9} + \frac{1}{12} & = \frac{ 1 \cdot \color{blue}{ 4 }}{ 9 \cdot \color{blue}{ 4 }} + \frac{ 1 \cdot \color{blue}{ 3 }}{ 12 \cdot \color{blue}{ 3 }} = \\[1ex] &=\frac{ \color{purple}{ 4 } }{ 36 } + \frac{ \color{purple}{ 3 } }{ 36 }=\frac{ \color{purple}{ 7 } }{ 36 } \end{aligned} $$

Divide $ \dfrac{9x-8}{144} $ by $ \dfrac{7}{36} $ to get $ \dfrac{ 324x-288 }{ 1008 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{9x-8}{144} }{ \frac{\color{blue}{7}}{\color{blue}{36}} } & \xlongequal{\text{Step 1}} \frac{9x-8}{144} \cdot \frac{\color{blue}{36}}{\color{blue}{7}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 9x-8 \right) \cdot 36 }{ 144 \cdot 7 } \xlongequal{\text{Step 3}} \frac{ 324x-288 }{ 1008 } \end{aligned} $$