1. **State the problem:** Simplify the expression $\frac{18x}{6x}$. 2. **Recall the rule:** When dividing fractions or terms, divide the numerators and denominators separately. Also, if the same variable appears in numerator and denominator, it can be canceled out, provided it is not zero. 3. **Write the fraction:** $$\frac{18x}{6x}$$ 4. **Cancel common factors:** Both numerator and denominator have a factor of $6x$. $$\frac{\cancel{6} \times 3 \times \cancel{x}}{\cancel{6} \times 1 \times \cancel{x}}$$ 5. **Simplify the fraction:** $$\frac{3}{1} = 3$$ 6. **State the restriction:** Since we canceled $x$, $x \neq 0$. 7. **Final answer:** $$3, \quad x \neq 0$$