SOLUTION: How would I perform this indicated operation?
4 / [sqrt(11) + sqrt(3)] – 2 / [sqrt(11) – sqrt(3)]
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Question 311059: How would I perform this indicated operation?
4 / [sqrt(11) + sqrt(3)] – 2 / [sqrt(11) – sqrt(3)]
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You have radicals in the denominators, and you have different denominators. Fortunately, both of these little problems can be eliminated by one operation. The LCD of the two fractions is simply the product of the two denominators, but since the two denominators are conjugates, each is precisely the appropriate multiplier to rationalize the other.
Proceed thus:
\left(\frac{\sqrt{11}-\sqrt{3}}{\sqrt{11}-\sqrt{3}}\right)\ -\ \left(\frac{2}{\sqrt{11}-\sqrt{3}}\right)\left(\frac{\sqrt{11}+\sqrt{3}}{\sqrt{11}+\sqrt{3}}\right))
The product of a conjugate pair is the difference of two squares, so:
}{11\ -\ 3}\ -\ \frac{2(\sqrt{11}+\sqrt{3})}{11\ -\ 3})
John
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