The expression you provided is:

\[
\frac{1}{7x} - \frac{5x + y}{7xy}
\]

To simplify this expression, we first need to find a common denominator. The denominators are \(7x\) and \(7xy\), so the least common denominator (LCD) is \(7xy\).

### Step-by-step solution:

1. **Rewrite each fraction with the common denominator:**

   - The first fraction \(\frac{1}{7x}\) needs to be rewritten with the denominator \(7xy\). We multiply both the numerator and denominator by \(y\):

   \[
   \frac{1}{7x} = \frac{1 \cdot y}{7x \cdot y} = \frac{y}{7xy}
   \]

   - The second fraction \(\frac{5x + y}{7xy}\) already has the denominator \(7xy\), so it remains unchanged.

2. **Combine the fractions:**

   Now that both fractions have the same denominator, we can subtract them:

   \[
   \frac{y}{7xy} - \frac{5x + y}{7xy} = \frac{y - (5x + y)}{7xy}
   \]

3. **Simplify the numerator:**

   Distribute the negative sign in the numerator:

   \[
   y - (5x + y) = y - 5x - y
   \]

   The \(y\) terms cancel out:

   \[
   y - y - 5x = -5x
   \]

4. **Final simplified expression:**

   The simplified expression is:

   \[
   \frac{-5x}{7xy}
   \]

   Simplifying further, the \(x\) in the numerator and denominator cancel out:

   \[
   \frac{-5}{7y}
   \]

So, the final simplified result is:

\[
\boxed{\frac{-5}{7y}}
\]

---

Would you like further details or have any questions? Here are some related questions to explore:

1. How do you find the least common denominator of two rational expressions?
2. How can you simplify rational expressions with variables in the denominator?
3. What happens when variables cancel out in the numerator and denominator?
4. How can negative signs be distributed in fractions?
5. What are common mistakes to avoid when simplifying rational expressions?

**Tip:** Always ensure that any variables in the denominator are non-zero to avoid undefined expressions!

Learn how to simplify the rational expression 1/7x - (5x + y)/7xy. This problem involves key algebraic concepts, including finding a common denominator, subtracting fractions, and simplifying the resulting expression. Ideal for students in Grades 8-10.

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