Exercise: Spivak's torture test

### Exercise: Spivak's torture test

Use LaTeX to typeset the following monstrosity, which is described by Michael Spivak in his book The Joy of TeX (second edition, page 123, Exercise 18.11) as "a virtual mine field of potential typing errors." Use \newcommand to define macros to simplify the typing.

Here are two stylistic points to keep in mind.

1. In compound fractions, the second-level fraction tends to be too small. If you type the second-level fraction as \displaystyle\frac instead of \frac, it will be bigger. (If you \usepackage{amsmath}, then you can type \dfrac instead of \displaystyle\frac.)

2. To get parentheses that adjust themselves to the size of the enclosed material, use \left( and \right) instead of just ( and ).