Simplifying Complex Fractions
Example 1
Simplify:

Solution |
 |
Step 1 Write the complex fraction
using a division symbol, ÷. |
 |
Step 2 Invert the second fraction and
change the division symbol, ÷, to the multiplication symbol,
·. |
 |
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, ÷. |
|
 |
Step 2 Invert the second fraction and
change the division symbol, ÷, to the multiplication symbol,
·. |
|
 |
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.)
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