1. First, recognize the forms of $F(x)$ and $G(x)$:
F(x) = \frac{2}{x}
G(x) = \frac{3}{x-1}
2. Multiply $F(x)$ by $G(x)$:
(F \cdot G)(x) = \frac{2}{x} \cdot \frac{3}{x-1}
3. Multiply the numerators and the denominators:
\frac{2 \cdot 3}{x \cdot (x-1)} = \frac{6}{x(x-1)}
4. The answer is:
\frac{6}{x(x-1)}