Question

Tìm các số nguyên x, y thỏa mãn điều kiện: \(\frac{3}{x}-\frac{7}{y}=2\).

Answer 1

\(\frac{3}{x}-\frac{7}{y}=2\)

\(\Rightarrow\frac{3}{x}=2+\frac{7}{y}\)

\(\Rightarrow\frac{3}{x}=\frac{2y}{y}+\frac{7}{y}\)

\(\Rightarrow\frac{3}{x}=\frac{2y+7}{y}\)

\(\Rightarrow2xy+7x=3y\)

\(\Rightarrow2xy+7x-3y=0\)

\(\Rightarrow4xy+14x-6y=0\)

\(\Rightarrow4xy+14x-6y-21=-21\)

\(\Rightarrow2x\left(2y+7\right)-3\left(2y+7\right)=-21\)

\(\Rightarrow\left(2x-3\right)\left(2y+7\right)=-21\)