Method 2:
This is one of two methods
for simplifying complex fractions.
Also see Method 1.


Remember ... a complex fraction is just a fraction
within a fraction. 


To Simplify a
Complex Fraction by Simplifying the Numerator and Denominator 
1. Create one single fraction in the numerator
(if necessary).
2. Create one single fraction in the denominator (if
necessary).
3. Remember the main fraction line
means "divide". Rewrite the fraction using
a division symbol
.
4. Follow the normal rules for dividing fractions: Invert the
the second term (the denominator of the complex fraction) and multiply (by
the numerator of the complex fraction).
5. Simplify if needed. 
Let's see Method 2
at work on the following problems:

Complex Fractions are EASY to simplify if you show your work!
Just
remember that the
fraction bar means DIVIDE.
Rewrite each fraction using a division symbol in the correct
position and solve as you would any other problem involving
fractions. 

1. 

Remember: when dividing fractions, invert (flip over) the second fraction and
multiply. Reduce the final answer if needed (or reduce as you
multiply). 
2. 

Remember: a mixed number
should be
converted to an improper fraction (heavier on top) before
simplifying. 
3. 

Remember:
change the numerator and denominator
to single fractions by creating a common denominator. The least common
denominator for the terms in this numerator is 32. The
least common
denominator for the terms in this denominator is 16.
(Note: the two common denominators used
to create the single fractions may, or may not, be the same
value. Most often they are NOT the same value.)


Remember:
invert the
second fraction and multiply.

Answer:

Remember:
it may be
necessary to factor to reduce a fraction.
Be sure that your
final answer is in simplest reduced form.



5. 

Remember:
in this problem, change the numerator to a
single fraction before you start to simplify. The least common
denominator for this numerator is x^{2}.
(The second term in the numerator will
need to be multiplied by x/x to create
the needed denominator.) 


Remember: combine
the terms in the numerator to form a single fraction in the
numerator of this problem. 


Remember: after
you invert the second fraction, multiply. 


Express the
final answer.
(When removing the parentheses
in the top, be sure to distribute the 6 ... multiply each term by
the 6.) 

Don't let
these fractions trip you up!
Just work carefully through
each problem, showing your work as you progress. 

