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Simplify \dfrac{1}{\sqrt2+sqrt3}+\dfrac{1}{\sqrt2-sqrt3}.

 May 5, 2024
 #1
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Here is my attempt.
To simplify the expression 12+3+123, we need to rationalize the denominators of the fractions.
 

Let's start by rationalizing the first fraction: 12+32323=2323=(23)=2+3

 

Next, rationalize the second fraction: 1232+32+3=2+323=(2+3)=23

 

Now, add the two rationalized fractions together:2+3+(23)=2+323=22

 

 

Therefore, the simplified expression is 22.

 May 5, 2024

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