Answer:
Step-by-step explanation:
[tex]\left(3+\frac{\frac{9}{2}}{\sqrt{5}}\right)\left(2-\sqrt{5}\right)n+\left(3-\frac{\frac{9}{2}}{\sqrt{5}}\right)\left(2+\sqrt{5}\right)[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\times \:a}[/tex]
[tex]=\left(\frac{9}{2\sqrt{5}}+3\right)\left(2-\sqrt{5}\right)n+\left(-\frac{\frac{9}{2}}{\sqrt{5}}+3\right)\left(2+\sqrt{5}\right)[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\times \:a}[/tex]
[tex]=\left(\frac{9}{2\sqrt{5}}+3\right)\left(2-\sqrt{5}\right)n+\left(-\frac{9}{2\sqrt{5}}+3\right)\left(2+\sqrt{5}\right)[/tex]
[tex]=\frac{-12-9\sqrt{5}}{2\sqrt{5}}n+6n+\left(3-\frac{9}{2\sqrt{5}}\right)\left(2+\sqrt{5}\right)[/tex]
[tex]=\frac{-12-9\sqrt{5}}{2\sqrt{5}}n+6n+\frac{12-9\sqrt{5}}{2\sqrt{5}}+6[/tex]
[tex]=\frac{\sqrt{5}\left(\left(3\sqrt{5}-12\right)n+12-9\sqrt{5}\right)}{10}+6[/tex]
