Zad. 30
[tex]\sqrt{3} *x-\frac{1}{\sqrt{12} } =\frac{1}{\sqrt{3} }[/tex]
[tex]\sqrt{3} *x-\frac{1}{2\sqrt{3} } =\frac{1}{\sqrt{3} }[/tex]
[tex]\sqrt{3} *x =\frac{3}{2\sqrt{3} }\ \ \ \ \ \ |*\sqrt{3}[/tex]
[tex]3 *x =\frac{3}{2 }\ \ \ \ \ \ |:3[/tex]
[tex]x=\frac{1}{2}[/tex]
Zad. 31
a)
[tex]\frac{4}{\sqrt{2} +\sqrt{8} } = \frac{4}{\sqrt{2} +2\sqrt{2} } = \frac{4}{3\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} } = \frac{4\sqrt{2} }{6} = \frac{2\sqrt{2} }{3}[/tex]
b)
[tex]\frac{16}{\sqrt{12} +\sqrt{75} } = \frac{16}{2\sqrt{3} +5\sqrt{3} } = \frac{16}{7\sqrt{3} } * \frac{\sqrt{3} }{\sqrt{3} } = \frac{16\sqrt{3} }{21 }[/tex]
c)
[tex]\frac{1}{\sqrt{5}+\sqrt{20}+\sqrt{45} } = \frac{1}{\sqrt{5}+2\sqrt{5}+3\sqrt{5} } = \frac{1}{6\sqrt{5} } * \frac{\sqrt{5} }{\sqrt{5} } = \frac{\sqrt{5} }{30}[/tex]
