Question: Solve $\dfrac{x}{4} - \dfrac{x-2}{8} = 5$.

Step 1. Bring both fractions to the common denominator $8$:

$$\dfrac{2x}{8} - \dfrac{x-2}{8} = 5$$

Step 2. Combine — keeping the second numerator in a bracket:

$$\dfrac{2x - (x-2)}{8} = 5 \;\Rightarrow\; \dfrac{2x - x + 2}{8} = 5 \;\Rightarrow\; \dfrac{x+2}{8} = 5$$

Step 3. Multiply up:

$$x + 2 = 40$$

Step 4.

$$x = 38$$

Check. $\dfrac{38}{4} - \dfrac{36}{8} = 9.5 - 4.5 = 5$. ✓

(Equally valid: multiply the whole equation by $8$ at the start — $2x - (x-2) = 40$ — same bracket, same answer.)

The same two routes (combine-first or clear-denominators-first) work on every fraction equation; pick whichever keeps the numbers smaller and carry brackets until the signs are resolved.

⚠ Watch out: The subtraction applies to the whole numerator: $-(x-2) = -x + 2$, not $-x - 2$ — this single sign is the most-lost mark in fraction equations. Multiply every term by the denominator, including the lonely $5$ on the right.