[tex]\displaystyle \frac{x^2+x-6}{x^2-7x+10}=\frac{x^2+3x-2x-6}{x^2-2x-5x+10}=\frac{x(x+3)-2(x+3)}{x(x-2)-5(x-2)}=\frac{(x+3)(x-2)}{(x-2)(x-5)}=\frac{x+3}{x-5}[/tex]