Question

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Answer 1

8) \(\dfrac{3\sqrt{2}-6}{\sqrt{2}-1}+\dfrac{6\sqrt{2}-4}{\sqrt{2}-3}\)

\(=\dfrac{\left(3\sqrt{2}-6\right)\left(\sqrt{2}+1\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}+\dfrac{\left(6\sqrt{2}-4\right)\left(\sqrt{2}+3\right)}{\left(\sqrt{2}-3\right)\left(\sqrt{2}+3\right)}\)

\(=\dfrac{6+3\sqrt{2}-6\sqrt{2}-6}{2-1}+\dfrac{12+18\sqrt{2}-4\sqrt{2}-12}{2-9}\)

\(=-3\sqrt{2}+\dfrac{14\sqrt{2}}{7}\)

\(=-3\sqrt{2}+2\sqrt{2}\)

\(=-\sqrt{2}\)