$$\frac { 4 + 3 \sqrt { 5 } } { 4 - 3 \sqrt { 5 } }$$
$\frac{-24\sqrt{5}-61}{29}\approx -3.953987292$
$$\frac{\left(4+3\sqrt{5}\right)\left(4+3\sqrt{5}\right)}{\left(4-3\sqrt{5}\right)\left(4+3\sqrt{5}\right)}$$
$$\frac{\left(4+3\sqrt{5}\right)\left(4+3\sqrt{5}\right)}{4^{2}-\left(-3\sqrt{5}\right)^{2}}$$
$$\frac{\left(4+3\sqrt{5}\right)^{2}}{4^{2}-\left(-3\sqrt{5}\right)^{2}}$$
$$\frac{16+24\sqrt{5}+9\left(\sqrt{5}\right)^{2}}{4^{2}-\left(-3\sqrt{5}\right)^{2}}$$
$$\frac{16+24\sqrt{5}+9\times 5}{4^{2}-\left(-3\sqrt{5}\right)^{2}}$$
$$\frac{16+24\sqrt{5}+45}{4^{2}-\left(-3\sqrt{5}\right)^{2}}$$
$$\frac{61+24\sqrt{5}}{4^{2}-\left(-3\sqrt{5}\right)^{2}}$$
$$\frac{61+24\sqrt{5}}{16-\left(-3\sqrt{5}\right)^{2}}$$
$$\frac{61+24\sqrt{5}}{16-\left(-3\right)^{2}\left(\sqrt{5}\right)^{2}}$$
$$\frac{61+24\sqrt{5}}{16-9\left(\sqrt{5}\right)^{2}}$$
$$\frac{61+24\sqrt{5}}{16-9\times 5}$$
$$\frac{61+24\sqrt{5}}{16-45}$$
$$\frac{61+24\sqrt{5}}{-29}$$
$$\frac{-61-24\sqrt{5}}{29}$$
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