Bài giải:

$B=\frac{1}{x-y}-\frac{3xy}{{{x}^{3}}-{{y}^{3}}}+\frac{x-y}{{{x}^{2}}+xy+{{y}^{2}}}$

=$\frac{1}{x-y}-\frac{3xy}{\left( x-y \right)\left( {{x}^{2}}+xy+{{y}^{2}} \right)}+\frac{x-y}{{{x}^{2}}+xy+{{y}^{2}}}$

=$\frac{{{x}^{2}}+xy+{{y}^{2}}-3xy+{{\left( x-y \right)}^{2}}}{\left( x-y \right)\left( {{x}^{2}}+xy+{{y}^{2}} \right)}$

=$\frac{2{{x}^{2}}+2{{y}^{2}}-4xy}{\left( x-y \right)\left( {{x}^{2}}+xy+{{y}^{2}} \right)}$

=$\frac{2\left( {{x}^{2}}-2xy+{{y}^{2}} \right)}{\left( x-y \right)\left( {{x}^{2}}+xy+{{y}^{2}} \right)}$

=$\frac{2{{\left( x-y \right)}^{2}}}{\left( x-y \right)\left( {{x}^{2}}+xy+{{y}^{2}} \right)}$

=$\frac{2\left( x-y \right)}{{{x}^{2}}+xy+{{y}^{2}}}$

Thay x=10, y=9 vào ta được $B=\frac{2\left( 10-9 \right)}{{{10}^{2}}+10.9+{{9}^{2}}}=\frac{2}{271}$