a: \(\left\{{}\begin{matrix}\dfrac{1}{x}-\dfrac{1}{y}=1\\\dfrac{2}{x}+\dfrac{3}{y}=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{2}{x}-\dfrac{2}{y}=2\\\dfrac{2}{x}+\dfrac{3}{y}=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-\dfrac{5}{y}=-3\\\dfrac{1}{x}-\dfrac{1}{y}=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=\dfrac{5}{3}\\\dfrac{1}{x}=1+\dfrac{1}{y}=1+\dfrac{3}{5}=\dfrac{8}{5}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=\dfrac{5}{3}\\x=\dfrac{5}{8}\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}\dfrac{15}{x}-\dfrac{7}{y}=9\\\dfrac{4}{x}+\dfrac{9}{y}=35\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{60}{x}-\dfrac{28}{y}=36\\\dfrac{60}{x}+\dfrac{135}{y}=525\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-\dfrac{163}{y}=-489\\\dfrac{15}{x}-\dfrac{7}{y}=9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=\dfrac{1}{3}\\\dfrac{15}{x}=9+\dfrac{7}{y}=9+21=30\end{matrix}\right.\)
=>x=1/2 và y=1/3
c: \(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=5\\\dfrac{2}{x}+\dfrac{5}{y}=7\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{2}{x}+\dfrac{2}{y}=10\\\dfrac{2}{x}+\dfrac{5}{y}=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-\dfrac{3}{y}=3\\\dfrac{1}{x}+\dfrac{1}{y}=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=-1\\\dfrac{1}{x}=5-\dfrac{1}{y}=5+1=6\end{matrix}\right.\)
=>x=1/6 và y=-1
d: \(\left\{{}\begin{matrix}\dfrac{1}{x+y}+\dfrac{1}{x-y}=\dfrac{5}{8}\\\dfrac{1}{x+y}-\dfrac{1}{x-y}=-\dfrac{3}{8}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{2}{x+y}=\dfrac{5}{8}-\dfrac{3}{8}=\dfrac{2}{8}\\\dfrac{1}{x+y}-\dfrac{1}{x-y}=-\dfrac{3}{8}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+y=8\\\dfrac{1}{x-y}=\dfrac{1}{x+y}+\dfrac{3}{8}=\dfrac{1}{8}+\dfrac{3}{8}=\dfrac{4}{8}=\dfrac{1}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+y=8\\x-y=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=10\\x-y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=5\\y=5-2=3\end{matrix}\right.\)
e: \(\left\{{}\begin{matrix}\dfrac{1}{x-1}+\dfrac{1}{y-1}=2\\\dfrac{1}{x-1}-\dfrac{3}{y-1}=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{4}{x-1}=1\\\dfrac{1}{x-1}+\dfrac{1}{y-1}=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-1=4\\\dfrac{1}{y-1}=2-\dfrac{1}{x-1}=2-\dfrac{1}{4}=\dfrac{7}{4}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=5\\y-1=\dfrac{4}{7}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=5\\y=\dfrac{11}{7}\end{matrix}\right.\)
