The given expression is:

\[
\frac{X - y}{4} - \frac{2x + y}{8}
\]

We can simplify it by finding a common denominator. The common denominator between 4 and 8 is 8. So, we rewrite the first fraction with a denominator of 8:

\[
\frac{X - y}{4} = \frac{2(X - y)}{8}
\]

Now, the expression becomes:

\[
\frac{2(X - y)}{8} - \frac{2x + y}{8}
\]

Since both fractions now have the same denominator, we can combine them:

\[
\frac{2(X - y) - (2x + y)}{8}
\]

Now, expand the terms in the numerator:

\[
2(X - y) = 2X - 2y
\]

Substitute this back into the equation:

\[
\frac{(2X - 2y) - (2x + y)}{8} = \frac{2X - 2y - 2x - y}{8}
\]

Simplify the terms in the numerator:

\[
\frac{2X - 2x - 3y}{8}
\]

So, the simplified expression is:

\[
\frac{2(X - x) - 3y}{8}
\]

Would you like further details or clarifications on this?

Here are five related questions to explore:
1. What happens if we substitute specific values for \(X\), \(x\), and \(y\)?
2. How would the process change if we had different denominators?
3. Can this expression be factored further or solved for a variable?
4. How does this method generalize to expressions with more terms?
5. What happens if the variables involve exponents?

**Tip:** Always look for common denominators to simplify algebraic fractions efficiently.

Learn how to simplify the algebraic expression (X - y) / 4 - (2x + y) / 8 by finding a common denominator and combining terms. This step-by-step guide covers key algebraic concepts and is suitable for students in Grades 8-10.

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