As much as it embarasses me to say it, but I always had a hard time understanding the following equality:
$ \frac{a}{\frac{b}{x}} = x \times \frac{a}{b} $
I always thought that the left-hand side of the above equation was equivalent to
$ \frac{a}{\frac{b}{x}} = \frac{a}{b} \div \frac{x}{1} = \frac{a}{b} \times \frac{1}{x} $
What am I doing wrong, here?