To simplify the expression \( \frac{x}{3} \div 4x \), we can rewrite the division as multiplication by the reciprocal:
\[ \frac{x}{3} \div 4x = \frac{x}{3} \times \frac{1}{4x} \]
Now, we multiply the fractions:
\[ \frac{x \cdot 1}{3 \cdot 4x} = \frac{x}{12x} \]
Next, we can simplify \( \frac{x}{12x} \). Since \( x \) is in both the numerator and the denominator, we can cancel it out (assuming \( x \neq 0 \)):
\[ \frac{x}{12x} = \frac{1}{12} \]
Thus, the expression \( \frac{x}{3} \div 4x \) simplifies to:
\[ \frac{1}{12} \]
So, the final equivalent expression is:
\[ \frac{1}{12} \]
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