[tex]\frac2{x-4}-\frac3{x-1}\\\\(x-4)(x-1)\neq0\\x-4 \neq 0 /+4\\x \neq 4\\\\x-1 \neq 0 /+1\\x \neq 1\\\\D \in R /\{1, 4\}[/tex]
[tex]\frac2{x-4}-\frac3{x-1}=\frac{2(x-1)}{(x-4)(x-1)}-\frac{3(x-4)}{(x-4)(x-1)}=\frac{2x-2-(3x-12)}{x^2-x-4x+4}=\frac{2x-2-3x+12}{x^2-5x+4}=\frac{-x+10}{x^2-5x+4}=\frac{-(x-10)}{x^2-5x+4}=-\frac{x-10}{x^2-5x+4}[/tex]
