#### Answer

$\dfrac{2}{x-3}-\dfrac{4}{x-1}=-\dfrac{2(x-5)}{(x-3)(x-1)}$

#### Work Step by Step

$\dfrac{2}{x-3}-\dfrac{4}{x-1}$
Evaluate the substraction of the two rational expressions:
$\dfrac{2}{x-3}-\dfrac{4}{x-1}=\dfrac{2(x-1)-4(x-3)}{(x-3)(x-1)}=\dfrac{2x-2-4x+12}{(x-3)(x-1)}=...$
$...=\dfrac{-2x+10}{(x-3)(x-1)}=...$
Take out common factor $-2$ from the numerator to provide a more simplified answer:
$...=-\dfrac{2(x-5)}{(x-3)(x-1)}$