[tex]\displaystyle\bf\\1)\\\\\frac{7}{a+7} +\frac{a^{2} +49}{a^{2} -49} -\frac{7}{a-7} =\frac{7}{a+7} +\frac{a^{2} +49}{(a -7)\cdot(a+7)} -\frac{7}{a-7} =\\\\\\=\frac{7\cdot(a-7)+a^{2} +49-7\cdot(a+7)}{(a-7)\cdot(a+7)} =\\\\\\=\frac{7a-49+a^{2} +49-7a-49}{(a-7)\cdot(a+7)} =\frac{a^{2} -49}{a^{2} -49} =1\\\\2)\\\\1:\frac{a+1}{2} =1\cdot\frac{2}{a+1} =\frac{2}{a+1} \\\\\\Otvet \ : \ \frac{2}{a+1}[/tex]