Bài giải:

 $\left( \frac{5x+y}{{{x}^{2}}-5xy}+\frac{5x-y}{{{x}^{2}}+5xy} \right).\frac{{{x}^{2}}-25{{y}^{2}}}{{{x}^{2}}+{{y}^{2}}}$

=$\left( \frac{5x+y}{x\left( x-5y \right)}+\frac{5x-y}{x\left( x+5y \right)} \right).\frac{\left( x-5y \right)\left( x+5y \right)}{{{x}^{2}}+{{y}^{2}}}$

=$\frac{\left( 5x+y \right).\left( x+5y \right)+\left( 5x-y \right)\left( x-5y \right)}{x\left( x-5y \right)\left( x+5y \right)}.\frac{\left( x-5y \right)\left( x+5y \right)}{{{x}^{2}}+{{y}^{2}}}$

=$\frac{10\left( {{x}^{2}}+{{y}^{2}} \right)}{x\left( {{x}^{2}}+{{y}^{2}} \right)}=\frac{10}{x}$

Trả lời:10/x