Multiply $ \dfrac{2}{5} $ by $ x $ to get $ \dfrac{ 2x }{ 5 } $.

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.

$$ \begin{aligned} \frac{2}{5} \cdot x & \xlongequal{\text{Step 1}} \frac{2}{5} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2 \cdot x }{ 5 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 2x }{ 5 } \end{aligned} $$

Subtract $4$ from $ \dfrac{7}{x} $ to get $ \dfrac{ \color{purple}{ -4x+7 } }{ x }$.

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

$$ \begin{aligned} \frac{7}{x} -4 & \xlongequal{\text{Step 1}} \frac{7}{x} - \frac{4}{\color{red}{1}} = \frac{ 7 }{ x } - \frac{ 4 \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7 } }{ x } - \frac{ \color{purple}{ 4x } }{ x }=\frac{ \color{purple}{ -4x+7 } }{ x } \end{aligned} $$

Subtract $20$ from $ \dfrac{2x}{5} $ to get $ \dfrac{ \color{purple}{ 2x-100 } }{ 5 }$.

Step 1: Write $ 20 $ 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 $\color{blue}{5}$.

$$ \begin{aligned} \frac{2x}{5} -20 & \xlongequal{\text{Step 1}} \frac{2x}{5} - \frac{20}{\color{red}{1}} = \frac{ 2x }{ 5 } - \frac{ 20 \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2x } }{ 5 } - \frac{ \color{purple}{ 100 } }{ 5 }=\frac{ \color{purple}{ 2x-100 } }{ 5 } \end{aligned} $$

Subtract $4$ from $ \dfrac{7}{x} $ to get $ \dfrac{ \color{purple}{ -4x+7 } }{ x }$.

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

$$ \begin{aligned} \frac{7}{x} -4 & \xlongequal{\text{Step 1}} \frac{7}{x} - \frac{4}{\color{red}{1}} = \frac{ 7 }{ x } - \frac{ 4 \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7 } }{ x } - \frac{ \color{purple}{ 4x } }{ x }=\frac{ \color{purple}{ -4x+7 } }{ x } \end{aligned} $$

Add $ \dfrac{2x-100}{5} $ and $ \dfrac{-4x+7}{x} $ to get $ \dfrac{ \color{purple}{ 2x^2-120x+35 } }{ 5x }$.

To add 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 $\color{blue}{ 5 }$.

$$ \begin{aligned} \frac{2x-100}{5} + \frac{-4x+7}{x} & = \frac{ \left( 2x-100 \right) \cdot \color{blue}{ x }}{ 5 \cdot \color{blue}{ x }} + \frac{ \left( -4x+7 \right) \cdot \color{blue}{ 5 }}{ x \cdot \color{blue}{ 5 }} = \\[1ex] &=\frac{ \color{purple}{ 2x^2-100x } }{ 5x } + \frac{ \color{purple}{ -20x+35 } }{ 5x }=\frac{ \color{purple}{ 2x^2-120x+35 } }{ 5x } \end{aligned} $$