How does this separation of the variable from the fraction result in $3\cdot \frac{1}{x}$ & not $\frac{3}{x}$ I wish to write the following expression as the product of a whole number or a fraction and variable expression. The answer given in my textbook is as follows:
$\frac{3}{x} = \frac{3\cdot 1}{1\cdot x} = \frac{3}{1} \cdot \frac{1}{x} = 3\cdot \frac{1}{x} $
However, I am not sure how to get to $3\cdot \frac{1}{x} $. When I complete the multiplication I get to $\frac{3}{1} \cdot \frac{1}{x} = \frac{3}{x}$, which of course loops me back round!

The key is simply to notice that
$$\frac31=3$$
Thus,
$$\frac31\cdot\frac1x=3\cdot\frac1x$$
