Answer :
Explanation
[tex]\frac{2}{x^2+6x-7}+\frac{3}{x^2+8x+7}=\frac{6}{x^2-1}[/tex]Factoring:
[tex]\frac{2}{(x+7)(x-1)}+\frac{3}{(x+7)(x+1)}=\frac{6}{(x+1)(x-1)}[/tex][tex]\frac{2(x+7)(x+1)+3(x+7)(x-1)}{(x+7)(x+7)(x+1)(x-1)}=\frac{6}{(x+1)(x-1)}[/tex][tex]\frac{\left(x+1\right)\left(x-1\right)(2(x+7)(x+1)+3(x+7)(x-1))}{(x+7)(x+7)(x+1)(x-1)}=6[/tex][tex]\frac{2(x+7)(x+1)+3(x+7)(x-1)}{(x+7)(x+7)}=6[/tex][tex]\frac{(x+7){}(2(x+1)+3(x-1))}{(x+7)(x+7)}=6[/tex][tex]\frac{2(x+1)+3(x-1)}{(x+7)}=6[/tex][tex]\frac{2x+2+3x-3}{x+7}=6[/tex][tex]\frac{5x-1}{x+7}=6[/tex][tex]5x-1=6(x+7)[/tex][tex]5x-1=6x+42[/tex][tex]5x-6x=42+1[/tex][tex]-x=43[/tex][tex]x=-43[/tex]Answer
x=-43