a) $\frac{3}{x – 4}$ - $\frac{2}{4 – x}$ = $\frac{3}{x - 4}$ - $\frac{-2}{x - 4}$ = $\frac{3 – (-2)}{x - 4}$ = $\frac{5}{x - 4}$;             

b) $\frac{x + 2}{x – 1}$ - $\frac{x – 9}{1 – x}$ - $\frac{x – 9}{1 – x}$ = $\frac{-(x + 2)}{1 - x}$ - $\frac{x – 9}{1 – x}$ - $\frac{x – 9}{1 – x}$ = $\frac{-x – 2 – (x – 9) – (x – 9)}{1 – x}$ = $\frac{-3x + 16}{1 – x}$;              

c) $\frac{x + 3}{x^{2} - 1}$ - $\frac{x + 1}{x^{2} – x}$ = $\frac{x + 3}{(x – 1)(x + 1)}$ - $\frac{x + 1}{x(x – 1)}$ = $\frac{x(x + 3)}{x(x – 1)(x + 1)}$ - $\frac{(x + 1)(x + 1)}{x(x – 1)(x + 1)}$

= $\frac{x^{2} + 3x – (x^{2} + 2x + 1)}{x(x – 1)(x + 1)}$ = $\frac{x - 1}{x(x – 1)(x + 1)}$ = $\frac{1}{x(x + 1)}$.