$$\frac{ \sqrt{ 2 } + \sqrt{ 3 } }{ \sqrt{ 2 } -1 }$$
$\sqrt{2}+\sqrt{3}+\sqrt{6}+2\approx 7.595754113$
$$\frac{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}+1\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}$$
$$\frac{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}+1\right)}{\left(\sqrt{2}\right)^{2}-1^{2}}$$
$$\frac{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}+1\right)}{2-1}$$
$$\frac{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}+1\right)}{1}$$
$$\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}+1\right)$$
$$\left(\sqrt{2}\right)^{2}+\sqrt{2}+\sqrt{3}\sqrt{2}+\sqrt{3}$$
$$2+\sqrt{2}+\sqrt{3}\sqrt{2}+\sqrt{3}$$
$$2+\sqrt{2}+\sqrt{6}+\sqrt{3}$$
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