[tex]\displaystyle\bf\\\frac{6a^{2}+12a+6}{a^{2}-1 } =\frac{6(a^{2}+2a+1) }{(a-1)(a+1)} =\frac{6(a+1)^{2} }{(a-1)(a+1)}=\frac{6(a+1)}{a-1}[/tex]