Simplifying Complex Fractions
Example 1
Simplify:
![](./articles_imgs/1005/simpli45.gif)
Solution |
![](./articles_imgs/1005/simpli46.gif) |
Step 1 Write the complex fraction
using a division symbol, ÷. |
![](./articles_imgs/1005/simpli47.gif) |
Step 2 Invert the second fraction and
change the division symbol, ÷, to the multiplication symbol,
·. |
![](./articles_imgs/1005/simpli48.gif) |
Step 3 Factor the numerators and
denominators.
|
![](./articles_imgs/1005/simpli49.gif) |
Step 4 Cancel all pairs of factors
common to the numerators and
denominators. |
![](./articles_imgs/1005/simpli50.gif) |
Step 5 Multiply the numerators.
Multiply the denominators. |
![](./articles_imgs/1005/simpli51.gif) |
Thus,
![](./articles_imgs/1005/simpli52.gif)
Example 2
Simplify:
![](./articles_imgs/1005/simpli53.gif)
Solution
|
|
![](./articles_imgs/1005/simpli54.gif) |
Step 1 Write the complex fraction
using a division symbol, ÷. |
|
![](./articles_imgs/1005/simpli55.gif) |
Step 2 Invert the second fraction and
change the division symbol, ÷, to the multiplication symbol,
·. |
|
![](./articles_imgs/1005/simpli56.gif) |
Step 3 Factor the numerators and
denominators.
|
|
![](./articles_imgs/1005/simpli57.gif) |
Step 4 Cancel all pairs of factors
common to the numerators and
denominators.
|
|
![](./articles_imgs/1005/simpli58.gif) |
Step 5 Multiply the numerators.
Multiply the denominators. |
|
![](./articles_imgs/1005/simpli59.gif) |
Thus,
![](./articles_imgs/1005/simpli60.gif)
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.)
|