Subtract $y$ from $ \dfrac{9}{x} $ to get $ \dfrac{ \color{purple}{ -xy+9 } }{ x }$.

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

$$ \begin{aligned} \frac{9}{x} -y & \xlongequal{\text{Step 1}} \frac{9}{x} - \frac{y}{\color{red}{1}} = \frac{ 9 }{ x } - \frac{ y \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9 } }{ x } - \frac{ \color{purple}{ xy } }{ x }=\frac{ \color{purple}{ -xy+9 } }{ x } \end{aligned} $$

Add $ \dfrac{-xy+9}{x} $ and $ \dfrac{4}{x} $ to get $ \dfrac{-xy+13}{x} $.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{-xy+9}{x} + \frac{4}{x} & = \frac{-xy+9}{\color{blue}{x}} + \frac{4}{\color{blue}{x}} =\frac{ -xy+9 + 4 }{ \color{blue}{ x }} = \\[1ex] &= \frac{-xy+13}{x} \end{aligned} $$

Subtract $y$ from $ \dfrac{-xy+13}{x} $ to get $ \dfrac{ \color{purple}{ -2xy+13 } }{ x }$.

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

$$ \begin{aligned} \frac{-xy+13}{x} -y & \xlongequal{\text{Step 1}} \frac{-xy+13}{x} - \frac{y}{\color{red}{1}} = \frac{ -xy+13 }{ x } - \frac{ y \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -xy+13 } }{ x } - \frac{ \color{purple}{ xy } }{ x }=\frac{ \color{purple}{ -2xy+13 } }{ x } \end{aligned} $$