a) x\ne0 , x\ne3
\frac{3-x}{x} * \frac{2x+6}{x^2-9}=\frac{(3-x)(2x+6)}{x(x^2-9)}=\frac{6x+18-2x^2-6x}{x^3-9x}=\frac{-2x^2+18}{x^3-9x}
b) x\ne 2
\frac{6}{x-2} : \frac{3}{4x-8}=\frac{6}{x-2}*\frac{4x-8}{3}=\frac{6(4x-8)}{3(x-2)}=\frac{2(4x-8)}{x-2}
c) x\ne1
\frac{3x-6}{x-1} + \frac{6x-1}{2x+2}=\frac{(3x-6)(2x+2)+(6x-1)(x-1)}{(x-1)(2x+2)}=
\frac{6x^2+6x-12x-12+6x^2-6x-x+1}{2x^2+2x-2x-2}=\frac{12x^2-13x-11}{2x^2-2}
d) x\ne4 , x\ne 1
\frac{2}{x-4} - \frac{3}{x-1}=\frac{2(x-1)-3(x-4)}{(x-4)(x-1)}=\frac{2x-2-3x+12}{x^2-x-4x+4}=\frac{10-x}{x^2-5x+4}