[tex]\displaystyle \frac{x+6}{x^2+19x+78}=\frac{x+6}{x^2+13x+6x+78}=\frac{x+6}{x(x+13)+6(x+13)}=\frac{x+6}{(x+13)(x+6)}=\\\frac{1}{x+13}[/tex]