Is multiplication of rational expressions commutative?

For example, if you have two rational expression of variable $x$, such as $\setminus \frac{f \left(x\right)}{g \left(x\right)}$ and $\setminus \frac{h \left(x\right)}{k \left(x\right)}$, their product will be $\setminus \frac{f \left(x\right) \setminus \cdot h \left(x\right)}{g \left(x\right) \setminus \cdot k \left(x\right)}$. Since both $f \left(x\right) \setminus \cdot h \left(x\right)$ and $g \left(x\right) \setminus \cdot k \left(x\right)$ are commutative, you get that $\setminus \frac{f \left(x\right) \setminus \cdot h \left(x\right)}{g \left(x\right) \setminus \cdot k \left(x\right)} = \setminus \frac{h \left(x\right) \setminus \cdot f \left(x\right)}{k \left(x\right) \setminus \cdot h \left(x\right)}$, and this last term is of course $\setminus \frac{h \left(x\right)}{k \left(x\right)} \setminus \cdot \setminus \frac{f \left(x\right)}{h \left(x\right)}$