If \(\left[\begin{array}{cc}x+y & 2 \\ 5 & x y\end{array}\right]=\left[\begin{array}{ll}6 & 2 \\ 5 & 8\e…

From equality of matrices:

\(x+y=6\)
\(xy=8\)
\(\frac{24}{x}+\frac{24}{y}=24\left(\frac{1}{x}+\frac{1}{y}\right)\)
\(\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}\)
\(\frac{x+y}{xy}=\frac{6}{8}=\frac{3}{4}\)
\(\Rightarrow 24\left(\frac{1}{x}+\frac{1}{y}\right)=24\cdot \frac{3}{4}=18\)