Rationalizing the Denominator
If an expression such as
appears in a denominator,
we can multiply both the numerator and denominator by its conjugate
to get a rational number in the denominator.
Example 1
Rationalizing the denominator using conjugates
Write in simplified form.
![](./articles_imgs/947/ration28.gif)
Solution
![](./articles_imgs/947/ration29.gif) |
![](./articles_imgs/947/ration30.gif) |
Multiply the numerator and denominator by
![](./articles_imgs/947/ration27.gif) |
|
![](./articles_imgs/947/ration31.gif) |
![](./articles_imgs/947/ration32.gif) |
|
![](./articles_imgs/947/ration33.gif) |
Simplify. |
![](./articles_imgs/947/ration34.gif) |
![](./articles_imgs/947/ration35.gif) |
Multiply the numerator and
denominator by
![](./articles_imgs/947/ration36.gif) |
|
![](./articles_imgs/947/ration37.gif) |
![](./articles_imgs/947/ration38.gif) |
Helpful hint
The expressions in Example 1
are the types of expressions
that you must simplify when
learning the quadratic formula.
|