a) $\frac{4x + 13}{5x(x – 7)}$ - $\frac{x - 48}{5x(7 – x)}$ = $\frac{4x + 13}{5x(x – 7)}$ + $\frac{x - 48}{5x(x – 7)}$ = $\frac{4x + 13 + x - 48}{5x(x – 7)}$ = $\frac{5x - 35}{5x(x – 7)}$ = $\frac{5(x – 7)}{5x(x – 7)}$ = $\frac{1}{x}$;  

b) $\frac{1}{x – 5x^{2}}$ - $\frac{25x - 15}{25x^{2} - 1}$ = $\frac{-1}{x(5x – 1)}$ - $\frac{25x - 15}{(5x + 1)(5x – 1)}$ = $\frac{-1(5x + 1)}{x(5x + 1)(5x – 1)}$ - $\frac{x(25x – 15)}{x(5x – 1)(5x + 1)}$

= $\frac{-5x – 1 – (25x^{2} – 15x)}{x(5x + 1)(5x – 1)}$ = $\frac{-25x^{2} + 10x - 1}{x(5x + 1)(5x – 1)}$ = $\frac{-(5x – 1)x^{2}}{x(5x + 1)(5x – 1)}$ = $\frac{-5x + 1}{x(5x + 1)}$.