SOAL D.
[tex]\frac{2 \sqrt{5}}{\sqrt{3} + 1} = \frac{2 \sqrt{5}}{\sqrt{3} + 1} \times \frac{\sqrt{3} - 1}{\sqrt{3} - 1} = \frac{(2 \sqrt{5})(\sqrt{3} - 1)}{(\sqrt{3} + 1)(\sqrt{3} - 1)} [/tex]
[tex]= \frac{2 \sqrt{15} - 2 \sqrt{5}}{\sqrt{9} - \sqrt{3} + \sqrt{3} - 1} [/tex]
[tex]= \frac{2 \sqrt{15} - 2 \sqrt{5}}{\sqrt{9} - 1} [/tex]
[tex]= \frac{2 \sqrt{15} - 2 \sqrt{5}}{3 - 1} = \frac{2 \sqrt{15} - 2 \sqrt{5}}{2} = \sqrt{15} - \sqrt{5} [/tex]
SOAL E.
[tex]\frac{1}{\sqrt{2} - 3 \sqrt{3}} = \frac{1}{\sqrt{2} - 3 \sqrt{3}} \times \frac{\sqrt{2} + 3 \sqrt{3}}{\sqrt{2} + 3 \sqrt{3}} = \frac{(1)(\sqrt{2} + 3 \sqrt{3})}{(\sqrt{2} - 3 \sqrt{3})(\sqrt{2} + 3 \sqrt{3})} [/tex]
[tex]= \frac{\sqrt{2} + 3 \sqrt{3}}{\sqrt{4} + 3 \sqrt{6} - 3 \sqrt{6} - 9 \sqrt{9}} [/tex]
[tex]= \frac{\sqrt{2} + 3 \sqrt{3}}{\sqrt{4} - 9 \sqrt{9}} = \frac{\sqrt{2} + 3 \sqrt{3}}{2 - 9 \times 3} = \frac{\sqrt{2} + 3 \sqrt{3}}{2 - 27} = - \frac{\sqrt{2} + 3 \sqrt{3}}{25}[/tex]
[answer.2.content]
