[tex]a)\\\frac{x^3+x^2-4x-4}{x^2+3x+2}=\frac{x^2(x+1)-4(x+1)}{x^2+x+2x+2}=\\\\=\frac{(x+1)(x^2-4)}{x(x+1)+2(x+1)}=\frac{(x+1)(x-2)(x+2)}{(x+1)(x+2)}=x-2\\\\x\neq -1,x\neq -2[/tex]
[tex]b)\\\frac{2x^2+4x-6}{x^3-3x^2-9x+27}=\frac{2x^2+6x-2x-6}{x^2(x-3)-9(x-3)}=\\\\\frac{2x(x+3)-2(x+3)}{x^2(x-3)-9(x-3)}=\frac{(x+3)(2x-2)}{(x-3)(x^2-9)}=\\\\\frac{2(x+3)(x-1)}{(x-3)(x-3)(x+3)}=\frac{2(x-1)}{(x-3)(x-3)}\\\\x\neq 3,x\neq -3[/tex]
