Question

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Answer 1

a) \(\dfrac{2}{x^2-y^2}\cdot\sqrt{3\cdot\dfrac{\left(x+y\right)^2}{2}}=\dfrac{2}{\left(x-y\right)\left(x+y\right)}\cdot\dfrac{\sqrt{3}}{\sqrt{2}}\left(x+y\right)=\dfrac{2\sqrt{3}\left(x+y\right)}{\sqrt{2}\left(x-y\right)\left(x+y\right)}=\dfrac{\sqrt{6}}{x-y}\)

b) \(\dfrac{2}{2a-1}\cdot\sqrt{5a^2\left(4a^2-4a+1\right)}=\dfrac{2}{2a-1}\cdot\dfrac{\sqrt{5}a\cdot\left(2a-1\right)}{1}=2\sqrt{5}a\)