\(C=\dfrac{2}{x^2-y^2}\sqrt{\dfrac{9\left(x^2+2xy+y^2\right)}{4}}\)

\(C=\dfrac{2}{\left(x-y\right)\left(x+y\right)}\sqrt{\dfrac{9}{4}}.\sqrt{x^2+2xy+y^2}\)

\(C=\dfrac{2}{\left(x-y\right)\left(x+y\right)}.\dfrac{3}{2}.\left(x+y\right)\)

\(C=\dfrac{3\left(x+y\right)}{\left(x-y\right)\left(x+y\right)}=\dfrac{3}{x-y}\)