[tex]\displaystyle \frac{3x+9}{x+1}+\frac{x-6}{x-1}=3,x\neq -1,x\neq 1\\ \\\frac{3x+9}{x+1}+\frac{x-6}{x-1}-3=0\\ \\\frac{(x-1)(3x+9)+(x+1)(x-6)-3(x+1)(x-1)}{(x+1)(x-1)}=0\\ \\\frac{3x^2+9x-3x-9+x^2-6x+x-6-3(x^2-1)}{(x+1)(x-1)}=0\\ \\\frac{3x^2+9x-3x-9+x^2-6x+x-6-3x^2+3}{(x+1)(x-1)}=0\\ \\\frac{-12+x^2+x}{(x+1)(x-1)}=0\\ \\-12+x^2+x=0\\ x-12+x^2=0\\ 4x-3x-12+x^2=0\\x(x+4)-3(x+4)=0\\(x+4)(x-3)=0\\x+4=0,x-3=0\\x_1=-4,x_2=3[/tex]