You provided the expression:

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

To simplify this expression, let's follow these steps:

### Step 1: Find a common denominator
The denominators are 4 and 8. The least common denominator is 8, so we rewrite the first fraction:

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

Now, the expression becomes:

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

### Step 2: Combine the fractions
Since both fractions now have the same denominator, we can subtract the numerators:

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

Distribute the negative sign:

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

### Step 3: Simplify the numerator
The \(2X\) terms cancel out, leaving:

\[
\frac{-2y - y}{8} = \frac{-3y}{8}
\]

### Final Answer:
The simplified expression is:

\[
\frac{-3y}{8}
\]

Would you like more details, or do you have any questions?

Here are 5 related questions to practice:

1. Simplify \(\frac{3a - b}{5} - \frac{4a + 2b}{10}\).
2. What is the least common denominator of \(\frac{X + y}{6}\) and \(\frac{2X - 3y}{9}\)?
3. Combine \(\frac{5x - 3}{7} + \frac{4x + 6}{14}\).
4. What is the process for subtracting algebraic fractions with different denominators?
5. How can you simplify complex rational expressions?

**Tip:** Always ensure to find the least common denominator when dealing with fractions!

Learn how to simplify the algebraic expression X-y / 4 - 2x+y / 8 with a step-by-step guide. This example demonstrates key algebraic concepts, including finding a common denominator and simplifying expressions. Perfect for students in Grades 7-9.

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