Simplify the expression $\frac{x}{2x^3 \cdot 3x}$.

1. Problem Description

Simplify the expression $\frac{x}{2x^3 \cdot 3x}$.

2. Solution Steps

First, simplify the denominator by multiplying the terms:

$2x^3 \cdot 3x = 2 \cdot 3 \cdot x^3 \cdot x = 6x^{3+1} = 6x^4$.

Now, we have the expression $\frac{x}{6x^4}$.

Next, we can simplify the fraction by dividing both the numerator and the denominator by $x$:

$\frac{x}{6x^4} = \frac{x^1}{6x^4} = \frac{1}{6x^{4-1}} = \frac{1}{6x^3}$.

3. Final Answer

$\frac{1}{6x^3}$