Question

Answer 1

a) \(\dfrac{1}{1-\sqrt{2}}-\dfrac{1}{1+\sqrt{2}}\\ =\dfrac{1+\sqrt{2}}{\left(1-\sqrt{2}\right)\left(1+\sqrt{2}\right)}-\dfrac{1-\sqrt{2}}{\left(1-\sqrt{2}\right)\left(1+\sqrt{2}\right)}\\ =\dfrac{1+\sqrt{2}-1+\sqrt{2}}{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)}=\dfrac{2\sqrt{2}}{1-x}\)

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Answer 2

a: \(\dfrac{1}{1-\sqrt{2}}-\dfrac{1}{1+\sqrt{2}}=-1-\sqrt{2}+1-\sqrt{2}=-2\sqrt{2}\)

b: \(\dfrac{1}{\sqrt{2}-\sqrt{3}}-\dfrac{1}{\sqrt{3}+\sqrt{2}}=-\sqrt{3}-\sqrt{2}-\sqrt{3}+\sqrt{2}=-2\sqrt{3}\)