Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a...
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![Page 1: Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a single term denominator. We now turn our attention.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649d135503460f949e7528/html5/thumbnails/1.jpg)
Table of Contents
Rationalizing Denominators With Two Terms
• In a previous modules we rationalized a single term denominator. We now turn our attention to rationalizing two term denominators.
2
3 5
• Example 1
Rationalize the denominator:
![Page 2: Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a single term denominator. We now turn our attention.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649d135503460f949e7528/html5/thumbnails/2.jpg)
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2
3 5
What should be multiplied times the denominator to eliminate the radical?
3 3 5 3 3 3 5
3 5 3
The is still a radical in the result!
![Page 3: Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a single term denominator. We now turn our attention.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649d135503460f949e7528/html5/thumbnails/3.jpg)
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2
3 5
Try something a little different.
3 5 3 5
3 3 5 3 5 3 5 5
![Page 4: Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a single term denominator. We now turn our attention.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649d135503460f949e7528/html5/thumbnails/4.jpg)
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3 3 5 3 5 3 5 5
3 5 3 5 3 25
3 25
22
The radical has been eliminated!
![Page 5: Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a single term denominator. We now turn our attention.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649d135503460f949e7528/html5/thumbnails/5.jpg)
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The pattern we used was the original denominator
3 5 3 5
… times the same two term expression, except for the opposite sign.
These two expressions are called conjugates.
![Page 6: Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a single term denominator. We now turn our attention.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649d135503460f949e7528/html5/thumbnails/6.jpg)
Table of Contents
• To rationalize a two term denominator multiply both numerator and denominator by the conjugate of the denominator.
2
3 5
• Back to our original problem - rationalize the denominator
![Page 7: Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a single term denominator. We now turn our attention.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649d135503460f949e7528/html5/thumbnails/7.jpg)
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Multiply both numerator and denominator by the conjugate of the denominator.
2
3 53 5
3 5
2 3 5
22
Based on earlier work, we get …
3 5
11
11
3 5
11
5 3
11
or
![Page 8: Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a single term denominator. We now turn our attention.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649d135503460f949e7528/html5/thumbnails/8.jpg)
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• Example 2
Rationalize the denominator:
2 3
5 2
5 2
5 2
2 3 5 2
5 2 5 2
![Page 9: Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a single term denominator. We now turn our attention.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649d135503460f949e7528/html5/thumbnails/9.jpg)
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• Numerators:
2 3 5 2
2 5 2 2 3 5 3 2
2 5 2 2 15 6
![Page 10: Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a single term denominator. We now turn our attention.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649d135503460f949e7528/html5/thumbnails/10.jpg)
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• Denominators:
5 2 5 2
5 5 5 2 2 5 2 2
5 10 10 2
3
![Page 11: Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a single term denominator. We now turn our attention.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649d135503460f949e7528/html5/thumbnails/11.jpg)
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• Putting it back together …
2 3 5 2
5 2 5 2
2 5 2 2 15 6
3
![Page 12: Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a single term denominator. We now turn our attention.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649d135503460f949e7528/html5/thumbnails/12.jpg)
Table of Contents