Verified answer

[tex]\displaystyle\bf\\1)\\\\\frac{2a+1}{a^{2} -2a}+\frac{2a-1}{a^{2} +2a} = \frac{2a+1}{a\cdot(a -2)}+\frac{2a-1}{a\cdot(a+2)} = \\\\\\=\frac{(2a+1)\cdot(a+2)+(2a-1)\cdot(a-2)}{a(a-2)(a+2)} =\\\\\\=\frac{2a^{2} +4a+a+2+2a^{2} -4a-a+2}{a(a-2)(a+2)} =\\\\\\=\frac{4a^{2} +4}{a\cdot(a^{2} -4)} =\frac{4\cdot(a^{2}+1) }{a\cdot(a^{2} -4)} \\\\\\2)\\\\\frac{4\cdot(a^{2}+1) }{a\cdot(a^{2} -4)} \cdot\frac{a^{2} -4}{a^{2} +1} =\frac{4}{a} \\\\\\a=3^{-1} =\frac{1}{3}[/tex]

[tex]\displaystyle\bf\\\frac{4}{a} =\frac{4}{\frac{1}{3} } =4\cdot 3=12\\\\\\Otvet \ : \ 12[/tex]