Lời giải:
a)
$H=\frac{(x^2+y^2)(x+y)-x^2(x+1)-y^2(y-1)}{(x+1)(y-1)(x+y)}$
$=\frac{x^2y+xy^2-x^2+y^2}{(x+1)(y-1)(x+y)}$
$=\frac{xy(x+y)-(x-y)(x+y)}{(x+1)(y-1)(x+y)}=\frac{(x+y)(xy-x+y)}{(x+1)(y-1)(x+y)}$
$=\frac{xy-x+y}{(x+1)(y-1)}=\frac{xy-x+y}{xy-x+y-1}=1+\frac{1}{(x+1)(y-1)}$
b)
$H=6\Leftrightarrow \frac{1}{(x+1)(y-1)}=5$
$\Leftrightarrow (x+1)(y-1)=\frac{1}{5}$ (vô lý với mọi $x,y$ nguyên.