[tex]\displaystyle
a= \frac{\sqrt{27} +(-1) x^{2n+1} \sqrt{3} +(-1) x^{n} \sqrt{3}}{\sqrt{12} + (-1)^{2n} \sqrt{3}} = \\ \\
=\frac{3\sqrt{3} - x^{2n+1} \sqrt{3} -x^{n} \sqrt{3}}{2\sqrt{3} + \sqrt{3}} = \\ \\
=\frac{\sqrt{3}( 3 - x^{2n+1} -x^{n})}{3\sqrt{3} } =\\ \\
=\frac{ 3 - x^{2n+1} -x^{n}}{3 }[/tex]
