\(A=\frac{\left(x+5y\right)\left(x-5y\right)}{x^2+y^2}\left(\frac{5x-y}{x^2+5xy}+\frac{5x+y}{x^2-5xy}\right)\)
\(=\frac{\left(x+5y\right)\left(x-5y\right)}{x^2+y^2}\cdot\left(\frac{5x-y}{x\left(x+5y\right)}+\frac{5x+y}{x\left(x-5y\right)}\right)\)
\(=\frac{\left(x+5y\right)\left(x-5y\right)}{x^2+y^2}\cdot\frac{\left(5x-y\right)\left(x-5y\right)+\left(5x+y\right)\left(x+5y\right)}{x\left(x-5y\right)\left(x+5y\right)}\)
\(=\frac{1}{x^2+y^2}\cdot\frac{5x^2-25xy-xy+5y^2+5x^2+25xy+xy+5y^2}{x}\)
\(=\frac{1}{x^2+y^2}\cdot\frac{10x^2+10y^2}{x}=\frac{10}{x}\)
=10/0,987654321
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