$$\frac { 3 - \sqrt { 7 } } { 4 + \sqrt { 7 } }$$
$\frac{19-7\sqrt{7}}{9}\approx 0.053304536$
$$\frac{\left(3-\sqrt{7}\right)\left(4-\sqrt{7}\right)}{\left(4+\sqrt{7}\right)\left(4-\sqrt{7}\right)}$$
$$\frac{\left(3-\sqrt{7}\right)\left(4-\sqrt{7}\right)}{4^{2}-\left(\sqrt{7}\right)^{2}}$$
$$\frac{\left(3-\sqrt{7}\right)\left(4-\sqrt{7}\right)}{16-7}$$
$$\frac{\left(3-\sqrt{7}\right)\left(4-\sqrt{7}\right)}{9}$$
$$\frac{12-3\sqrt{7}-4\sqrt{7}+\left(\sqrt{7}\right)^{2}}{9}$$
$$\frac{12-7\sqrt{7}+\left(\sqrt{7}\right)^{2}}{9}$$
$$\frac{12-7\sqrt{7}+7}{9}$$
$$\frac{19-7\sqrt{7}}{9}$$
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