a/ $m=1$
$→\dfrac{x+1}{x+3}+\dfrac{x-3}{x-1}=2$ ($x\ne 1;-3$)
$↔\dfrac{(x+1)(x-1)+(x+3)(x-3)}{(x-1)(x+3)}=2$
$↔\dfrac{x²-1+x²-9}{x²-2x-3}=2$
$↔\dfrac{2x²-10}{x²-2x-3}=2$
$↔2x²-10=2x²-4x-6$
$↔4x=4$
$↔x=1$ (tm)
b/ Pt có nghiệm $x=2$
$→\dfrac{2+m}{5}+\dfrac{-1}{1}=2$
$↔\dfrac{2+m}{5}=3$
$↔2+m=15$
$↔m=13$