[tex]\displaystyle d). \frac{1- \sqrt{2} }{1+ \sqrt{2} } = \frac{(1- \sqrt{2} )(1- \sqrt{2} )}{1-2} = \frac{1- \sqrt{2}- \sqrt{2} +2 }{-1} = \frac{3-2 \sqrt{2} }{-1} = \\ \\ =- \frac{3-2 \sqrt{2} }{1} =2 \sqrt{2} -3[/tex]
[tex]\displaystyle e). \frac{7- \sqrt{5} }{3+ \sqrt{5} } = \frac{(7- \sqrt{5} )(3- \sqrt{5} )}{9-5} = \frac{21-7 \sqrt{5}-3 \sqrt{5}+5 }{4} = \\ \\ = \frac{26-10 \sqrt{5} }{4} = \frac{2(13-5 \sqrt{5} )}{4} = \frac{13-5 \sqrt{5} }{2} [/tex]
[tex]\displaystyle f). \frac{ \sqrt{3} }{ \sqrt{3} - \sqrt{2} } = \frac{ \sqrt{3} ( \sqrt{3} + \sqrt{2} )}{3-2} = \frac{3+ \sqrt{6} }{1} =3+ \sqrt{6} [/tex]
