[tex]\displaystyle\bf\\\frac{2a^{2} +4}{a^{2} -1} -\frac{a-2}{a+1} -\frac{a+1}{a-1} =\frac{2a^{2} +4}{(a -1)\cdot(a+1)} -\frac{a-2}{a+1} -\frac{a+1}{a-1} =\\\\\\=\frac{2a^{2} +4-(a-2)\cdot(a-1)-(a+1)\cdot(a+1)}{(a+1)(a-1)} =\\\\\\=\frac{2a^{2} +4-a^{2} +a+2a-2-a^{2}-2a-1 }{(a+1)(a-1)} =\\\\\\=\frac{a+1}{(a-1)\cdot(a+1)} =\frac{1}{a-1} \\\\\\\frac{1}{a-1 } = \frac{1}{a-1}[/tex]

Тождество доказано