Dividing Rational Expressions
Example 1
Find:
![](./articles_imgs/369/dividi25.gif)
Solution |
![](./articles_imgs/369/dividi26.gif) |
Step 1 Invert the second
fraction and change
the division symbol,
÷, to the multiplication
symbol, ·. |
![](./articles_imgs/369/dividi27.gif) |
Step 2 Factor the numerators
and denominators.
|
![](./articles_imgs/369/dividi28.gif) |
Step 3 Cancel all pairs of
factors common to the
numerators and
denominators. |
![](./articles_imgs/369/dividi29.gif) |
Step 4 Multiply the
numerators. Multiply
the denominators. |
![](./articles_imgs/369/dividi30.gif) |
Thus,
![](./articles_imgs/369/dividi31.gif)
Example 2
Find:
![](./articles_imgs/369/dividi32.gif)
Solution |
![](./articles_imgs/369/dividi33.gif) |
Step 1 Invert the second fraction
and change the division
symbol, ÷, to the
multiplication symbol, ·. |
![](./articles_imgs/369/dividi34.gif) |
Step 2 Factor the numerators and
denominators.
|
![](./articles_imgs/369/dividi35.gif) |
Step 3 Cancel all pairs of factors
common to the numerators
and denominators.
|
![](./articles_imgs/369/dividi36.gif) |
Step 4 Multiply the numerators.
Multiply the denominators. |
![](./articles_imgs/369/dividi37.gif) |
Thus,
![](./articles_imgs/369/dividi38.gif)
Notice that
is in lowest terms.
|