\(A=\dfrac{5x_1-x_2}{x_1}+\dfrac{5x_2-x_1}{x_2}\)
\(=\dfrac{5x_1\cdot x_2-x_2^2+5x_1x_2-x_1^2}{x_1x_2}\)
\(=\dfrac{10x_1x_2-\left[\left(x_1+x_2\right)^2-2x_1x_2\right]}{x_1x_2}\)
\(=\dfrac{10\cdot4-\left[5^2-2\cdot4\right]}{4}=\dfrac{40-25+8}{4}=\dfrac{23}{4}\)