Solution
Expression : $$\frac{\sqrt{43 - 12\sqrt{7}} - 2}{16 + 6\sqrt7}$$
= $$\frac{\sqrt{(\sqrt7)^2+(6)^2 - 2(\sqrt{7})(6)} - 2}{(\sqrt7)^2+(3)^2 + 2(\sqrt7)(3)}$$
= $$\frac{\sqrt{(6-\sqrt7)^2}-2}{(3+\sqrt7)^2}$$
= $$\frac{4-\sqrt7}{(3+\sqrt7)^2}$$
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Expression : $$\frac{\sqrt{43 - 12\sqrt{7}} - 2}{16 + 6\sqrt7}$$
= $$\frac{\sqrt{(\sqrt7)^2+(6)^2 - 2(\sqrt{7})(6)} - 2}{(\sqrt7)^2+(3)^2 + 2(\sqrt7)(3)}$$
= $$\frac{\sqrt{(6-\sqrt7)^2}-2}{(3+\sqrt7)^2}$$
= $$\frac{4-\sqrt7}{(3+\sqrt7)^2}$$
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