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Ta có: \(\dfrac{7}{15x}+\dfrac{9}{10y}=\dfrac{2}{5}-\dfrac{359}{30xy}\)
\(\Leftrightarrow\dfrac{14}{30xy}+\dfrac{27}{30xy}=\dfrac{12xy}{30xy}-\dfrac{359}{30xy}\)
\(\Leftrightarrow\dfrac{41}{30xy}=\dfrac{12xy-359}{30xy}\)
\(\Rightarrow12xy-359=41\)
\(\Rightarrow12xy=400\)
\(\Rightarrow xy=\dfrac{100}{3}\)
Vì \(x,y\in Z\) mà \(xy=\dfrac{100}{3}\)
\(\Rightarrow\) Phương trình vô nghiệm.
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\(\frac{3}{x}-\frac{7}{y}=2\)
\(\Rightarrow\frac{3}{x}=2+\frac{7}{y}\)
\(\Rightarrow\frac{3}{x}=\frac{2y}{y}+\frac{7}{y}\)
\(\Rightarrow\frac{3}{x}=\frac{2y+7}{y}\)
\(\Rightarrow2xy+7x=3y\)
\(\Rightarrow2xy+7x-3y=0\)
\(\Rightarrow4xy+14x-6y=0\)
\(\Rightarrow4xy+14x-6y-21=-21\)
\(\Rightarrow2x\left(2y+7\right)-3\left(2y+7\right)=-21\)
\(\Rightarrow\left(2x-3\right)\left(2y+7\right)=-21\)
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