Complex fractions are fractions that contain fractions in the numerator or denominator, e.g., (1/2)/3 and 1/(2/3) as well as (1/2)/(3/4) are complex fractions. To work with/simplify these fractions there is really only one rule to keep in mind:
```
(a/b)/(c/d) = (a/b)*(d/c)
```
when `b`, `c` and `d` are not 0. Namely, dividing by a fraction is the same thing as multiplying by it's [reciprocal](https://en.wikipedia.org/wiki/Multiplicative_inverse). To see this, note that multiplying both sides of our expression above by `c/d` gives
```
[(a/b)/(c/d)]*(c/d) = (a/b)
```
one the left, and
```
[(a/b)*(d/c)]*(c/d) = [(a*d)/(b*c)]*(c/d)
= (a*d*c)/(b*d*c*) = a/b
```
on the right, so going backwards and dividing `a/b` by `c/d` indeed gives the product `(a/b)*(d/c)`.
This extends to [real numbers](https://en.wikipedia.org/wiki/Real_number), [complex numbers](https://en.wikipedia.org/wiki/Complex_number) and [algebraic expressions](https://en.wikipedia.org/wiki/Algebraic_expression) as well. For example,
Note that in the example above we needed to get the numerator and denominator into a fractional form before being able to use the rule where division by a fraction is equivalent to multiplying by a denominator. Similarly, if we want to simplify
```
(1 + 1/2)/(2 + 2/3)
```
we must first simplify this into a fraction divided by another fraction to be able to use our rule above. We have
