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