Đáp án:
`e)` `\frac{\sqrt{21}}{7}`
`g)` `\frac{\sqrt{5}+2}{2}`
Giải thích các bước giải:
`e)` `\frac{\sqrt{15}-\sqrt{6}}{\sqrt{35}-\sqrt{14}}`
`=` `\frac{(\sqrt{15}-\sqrt{6})(\sqrt{35}+\sqrt{14})}{(\sqrt{35}-\sqrt{14})(\sqrt{35}+\sqrt{14})}`
`=` `\frac{(\sqrt{3}.\sqrt{5}-\sqrt{2}.\sqrt{3})(\sqrt{7}.\sqrt{5}+\sqrt{7}.\sqrt{2})}{(\sqrt{35})^2-(\sqrt{14})^2}`
`=` `\frac{\sqrt{3}(\sqrt{5}-\sqrt{2})\sqrt{7}(\sqrt{5}+\sqrt{2})}{35-14}`
`=` `\frac{\sqrt{3}.\sqrt{7}[(\sqrt{5})^2-(\sqrt{2})^2]}{21}`
`=` `\frac{\sqrt{21}(5-2)}{21}`
`=` `\frac{\sqrt{21}.3}{21}`
`=` `\frac{\sqrt{21}}{7}`
`g)` `\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}``-` `\frac{9-4\sqrt{5}}{2\sqrt{5}-4}`
`=` `\frac{\sqrt{5}(\sqrt{3}-1)}{\sqrt{3}-1}``-` `\frac{(\sqrt{5})^2-2.2\sqrt{5}+2^2}{2(\sqrt{5}-2)}`
`=` `\sqrt{5}``-``\frac{(\sqrt{5}-2)^2}{2(\sqrt{5}-2)}`
`=` `\sqrt{5}``-``\frac{\sqrt{5}-2}{2}`
`=` `\frac{\sqrt{5}.2}{2}``-``\frac{\sqrt{5}-2}{2}`
`=` `\frac{2\sqrt{5}-\sqrt{5}+2}{2}`
`=` `\frac{\sqrt{5}+2}{2}`
