d: \(\dfrac{\sqrt{6}+\sqrt{15}}{\sqrt{14}+\sqrt{35}}=\dfrac{\sqrt{21}}{7}\)
e: \(\dfrac{x-4\sqrt{x}+4}{x-4}=\dfrac{\sqrt{x}-2}{\sqrt{x}+2}\)
\(d,\dfrac{\sqrt{6}+\sqrt{15}}{\sqrt{14}+\sqrt{35}}=\dfrac{\left(\sqrt{6}+\sqrt{15}\right)\left(\sqrt{35}-\sqrt{14}\right)}{21}\\ =\dfrac{\sqrt{210}-2\sqrt{21}+5\sqrt{21}-\sqrt{210}}{21}=\dfrac{3\sqrt{21}}{21}\)
\(e,=\dfrac{\left(\sqrt{x}-2\right)^2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}-2}{\sqrt{x}+2}\\ f,=\dfrac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)-\sqrt{3}\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=1-\sqrt{3}\\ g,=\dfrac{3}{\left(x-y\right)\left(x+y\right)}\cdot\sqrt{\dfrac{16\left(x+y\right)^2}{9}}\\ =\dfrac{3}{\left(x-y\right)\left(x+y\right)}\cdot\dfrac{4\left(x+y\right)}{3}\\ =\dfrac{4}{x-y}\)
