$$\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$\frac{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$\frac{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$\frac{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{5-3}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$\frac{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$\frac{\left(\sqrt{5}+\sqrt{3}\right)^{2}}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$\frac{\left(\sqrt{5}\right)^{2}+2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$\frac{5+2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$\frac{5+2\sqrt{15}+\left(\sqrt{3}\right)^{2}}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$\frac{5+2\sqrt{15}+3}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$\frac{8+2\sqrt{15}}{2}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$4+\sqrt{15}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$4+\sqrt{15}+\frac{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$4+\sqrt{15}+\frac{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$4+\sqrt{15}+\frac{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}{5-3}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$4+\sqrt{15}+\frac{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}{2}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$4+\sqrt{15}+\frac{\left(\sqrt{5}-\sqrt{3}\right)^{2}}{2}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$4+\sqrt{15}+\frac{\left(\sqrt{5}\right)^{2}-2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}}{2}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$4+\sqrt{15}+\frac{5-2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}}{2}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$4+\sqrt{15}+\frac{5-2\sqrt{15}+\left(\sqrt{3}\right)^{2}}{2}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$4+\sqrt{15}+\frac{5-2\sqrt{15}+3}{2}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$4+\sqrt{15}+\frac{8-2\sqrt{15}}{2}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$4+\sqrt{15}+4-\sqrt{15}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$8+\sqrt{15}-\sqrt{15}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$8+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{3}{38+\sqrt{3}}$$

$$8+\frac{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}\times \frac{3}{38+\sqrt{3}}$$

$$8+\frac{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}}\times \frac{3}{38+\sqrt{3}}$$

$$8+\frac{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{5-3}\times \frac{3}{38+\sqrt{3}}$$

$$8+\frac{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{2}\times \frac{3}{38+\sqrt{3}}$$

$$8+\frac{\left(\sqrt{5}+\sqrt{3}\right)^{2}}{2}\times \frac{3}{38+\sqrt{3}}$$

$$8+\frac{\left(\sqrt{5}\right)^{2}+2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}}{2}\times \frac{3}{38+\sqrt{3}}$$

$$8+\frac{5+2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}}{2}\times \frac{3}{38+\sqrt{3}}$$

$$8+\frac{5+2\sqrt{15}+\left(\sqrt{3}\right)^{2}}{2}\times \frac{3}{38+\sqrt{3}}$$

$$8+\frac{5+2\sqrt{15}+3}{2}\times \frac{3}{38+\sqrt{3}}$$

$$8+\frac{8+2\sqrt{15}}{2}\times \frac{3}{38+\sqrt{3}}$$

$$8+\left(4+\sqrt{15}\right)\times \frac{3}{38+\sqrt{3}}$$

$$8+\left(4+\sqrt{15}\right)\times \frac{3\left(38-\sqrt{3}\right)}{\left(38+\sqrt{3}\right)\left(38-\sqrt{3}\right)}$$

$$8+\left(4+\sqrt{15}\right)\times \frac{3\left(38-\sqrt{3}\right)}{38^{2}-\left(\sqrt{3}\right)^{2}}$$

$$8+\left(4+\sqrt{15}\right)\times \frac{3\left(38-\sqrt{3}\right)}{1444-3}$$

$$8+\left(4+\sqrt{15}\right)\times \frac{3\left(38-\sqrt{3}\right)}{1441}$$

$$8+\frac{\left(4+\sqrt{15}\right)\times 3\left(38-\sqrt{3}\right)}{1441}$$

$$\frac{8\times 1441}{1441}+\frac{\left(4+\sqrt{15}\right)\times 3\left(38-\sqrt{3}\right)}{1441}$$

$$\frac{8\times 1441+\left(4+\sqrt{15}\right)\times 3\left(38-\sqrt{3}\right)}{1441}$$

$$\frac{11528+456-12\sqrt{3}+114\sqrt{15}-9\sqrt{5}}{1441}$$

$$\frac{11984-12\sqrt{3}+114\sqrt{15}-9\sqrt{5}}{1441}$$