The expression is:

\[
\frac{2a - b}{6} + \frac{a + b}{8}
\]

To simplify this, we need to combine the two fractions by finding a common denominator.

### Step 1: Find the common denominator
The denominators are 6 and 8. The least common denominator (LCD) of 6 and 8 is 24.

### Step 2: Rewrite the fractions with the common denominator

\[
\frac{2a - b}{6} = \frac{4(2a - b)}{24} = \frac{8a - 4b}{24}
\]

\[
\frac{a + b}{8} = \frac{3(a + b)}{24} = \frac{3a + 3b}{24}
\]

### Step 3: Combine the fractions

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

\[
\frac{8a - 4b}{24} + \frac{3a + 3b}{24} = \frac{(8a - 4b) + (3a + 3b)}{24}
\]

### Step 4: Simplify the numerator

Combine like terms:

\[
(8a + 3a) + (-4b + 3b) = 11a - b
\]

So the expression becomes:

\[
\frac{11a - b}{24}
\]

Thus, the simplified form of the given expression is:

\[
\frac{11a - b}{24}
\]

Would you like further details on any step or do you have any questions?

Here are five related questions for practice:
1. Simplify \(\frac{3x + 4}{5} + \frac{7x - 2}{10}\).
2. Combine \(\frac{2p - q}{9} + \frac{3p + 2q}{6}\).
3. Simplify \(\frac{4m - 5n}{8} - \frac{3m + 2n}{12}\).
4. What is the least common denominator of 9 and 15?
5. Expand and simplify \(\frac{2x - 3y}{5} + \frac{x + 4y}{10}\).

**Tip:** Always look for the least common denominator when adding or subtracting fractions!

Learn how to simplify the expression (2a - b) / 6 + (a + b) / 8 by finding the least common denominator and combining fractions step-by-step. This problem covers key algebraic concepts like fraction addition and simplification, suitable for students in Grades 7-9.

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