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

 Jun 8, 2024
 #1
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Let's first rationalize the denominators of the equations.

12+3=12+3×1=12+3×2323=23(2+3)×(23)=232232=2323=(23)=32

123=123×1=123×2+32+3=2+3(2+3)(23)=2+32232=2+323=(2+3)=23

 

Now we can see that the origional equation is just (sqrt(3) - sqrt(2)) + (-sqrt(2) - sqrt(3)). This simplifies to -2sqrt(2)

 Jun 9, 2024

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