The provided mathematical expression in the image is:

$B) \quad \frac{x - 4}{5} \cdot \frac{1}{x} + \frac{4}{5x}$

Let's simplify this step by step:

Step 1: Multiply the first term

The first term is: $\frac{x - 4}{5} \cdot \frac{1}{x} = \frac{(x - 4) \cdot 1}{5x} = \frac{x - 4}{5x}$

So, the expression becomes: $\frac{x - 4}{5x} + \frac{4}{5x}$

Step 2: Combine the fractions

Since both fractions have the same denominator $5x$, we can combine them directly: $\frac{x - 4}{5x} + \frac{4}{5x} = \frac{(x - 4) + 4}{5x}$

Simplify the numerator: $(x - 4) + 4 = x$

Thus, the combined fraction is: $\frac{x}{5x}$

Step 3: Simplify further

Cancel $x$ in the numerator and denominator (provided $x \neq 0$): $\frac{x}{5x} = \frac{1}{5}$

Final Answer:

$\boxed{\frac{1}{5}}$

Let me know if you'd like further clarification or have additional questions!

Related Questions:

1. How do you handle fractions with different denominators?
2. What is the domain of this expression? Why must $x \neq 0$?
3. How can we simplify more complex rational expressions?
4. Can you explain how to factor expressions like $x - 4$ if needed?
5. Why does $x$ cancel out when simplifying $\frac{x}{5x}$?

Tip:

Always check for restrictions on the variable (e.g., division by zero) before simplifying rational expressions.