A fraction that contains one or more fractions in its numerator and denominator is called a **complex fraction**. Examples are

A complex fraction may be simplified by reducing its numerator and denominator (separately) to simple fractions and then dividing.

__Example__:

Simplify the complex fraction

__Solution__:

** **

An alternative method for simplifying a complex fraction is to multiply its numerator and denominator by the LCD of all fractions occurring in its numerator and denominator. The resulting fraction may then be simplified by cancellation.

__Example__:

Simplify the complex fraction

__Solution__:The LCD of , , , and is . Therefore