Require non-zero Rational denominators.

This is amazing. Now, if you try to pass a 0 denominator, it'll
throw IllegalArgumentException.

The require() method is on the Predef object, which scala imports
for you for free.
Add fields numerator and denominator to Rational.

Also use these instance fields in toString instead of the clas
parameterse.
Add method add(that: Rational) to Rational.
Add method lessThan(that: Rational) to Rational.
Add method max(that: Rational) to Rational.

Most places, using "this" is optional. Here, however, the final
"this" is required, since you need to return the current object
if it is greater than the other, and "this" is the only way
to do that.
Add an auxilliary Rational constructor for whole numbers.

Instead of having to write new Rational(5, 1), now you can just
write new Rational(5).