a:
ĐKXĐ: x<>0 và y<>0
\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=2\\\dfrac{3}{x}-\dfrac{4}{y}=-1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{3}{x}+\dfrac{3}{y}=6\\\dfrac{3}{x}-\dfrac{4}{y}=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{7}{x}=7\\\dfrac{1}{x}+\dfrac{1}{y}=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=1\\\dfrac{1}{y}=2-\dfrac{1}{x}=1\end{matrix}\right.\)
=>x=1(nhận) và y=1(nhận)
b:
ĐKXĐ: x<>-2 và y<>0
\(\left\{{}\begin{matrix}\dfrac{7}{x+2}+\dfrac{3}{y}=2\\\dfrac{4}{x+2}-\dfrac{1}{y}=\dfrac{5}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{7}{x+2}+\dfrac{3}{y}=2\\\dfrac{12}{x+2}-\dfrac{3}{y}=\dfrac{15}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{19}{x+2}=\dfrac{19}{2}\\\dfrac{4}{x+2}-\dfrac{1}{y}=\dfrac{5}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+2=2\\\dfrac{1}{y}=\dfrac{4}{x+2}-\dfrac{5}{2}=-\dfrac{1}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=0\\y=-2\end{matrix}\right.\left(nhận\right)\)
c:
ĐKXĐ: \(\left\{{}\begin{matrix}x\ne-1\\y\ne-4\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{3x}{x+1}+\dfrac{2}{y+4}=4\\\dfrac{2x}{x+1}-\dfrac{5}{y+4}=9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{3x+3-3}{x+1}+\dfrac{2}{y+4}=4\\\dfrac{2x+2-2}{x+1}-\dfrac{5}{y+4}=9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3-\dfrac{3}{x+1}+\dfrac{2}{y+4}=4\\2-\dfrac{2}{x+1}-\dfrac{5}{y+4}=9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{3}{x+1}-\dfrac{2}{y+4}=3-4=-1\\\dfrac{2}{x+1}+\dfrac{5}{y+4}=-7\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{6}{x+1}-\dfrac{4}{y+4}=-2\\\dfrac{6}{x+1}+\dfrac{15}{y+4}=-21\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-\dfrac{19}{y+4}=19\\\dfrac{6}{x+1}+\dfrac{15}{y+4}=-21\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y+4=-1\\\dfrac{6}{x+1}=-21-\dfrac{15}{y+4}=-21+15=-6\end{matrix}\right.\)
=>x+1=-1 và y+4=-1
=>x=-2(nhận) và y=-5(nhận)
