Simplifying Complex Fractions
Example 1
Simplify:
Solution 

Step 1 Write the complex fraction
using a division symbol, Ã·. 

Step 2 Invert the second fraction and
change the division symbol, Ã·, to the multiplication symbol,
Â·. 

Step 3 Factor the numerators and
denominators.


Step 4 Cancel all pairs of factors
common to the numerators and
denominators. 

Step 5 Multiply the numerators.
Multiply the denominators. 

Thus,
Example 2
Simplify:
Solution



Step 1 Write the complex fraction
using a division symbol, Ã·. 


Step 2 Invert the second fraction and
change the division symbol, Ã·, to the multiplication symbol,
Â·. 


Step 3 Factor the numerators and
denominators.



Step 4 Cancel all pairs of factors
common to the numerators and
denominators.



Step 5 Multiply the numerators.
Multiply the denominators. 


Thus,
Note:
In
we cannot cancel x.
Although x is a factor of the numerator,
x is not a factor of the denominator.
(In the denominator, x is in a term,
not a factor.)
