\(\frac{x+2y}{4x-3y}\)=-2
\(\Rightarrow\)-2(4x-3y)=x+2y
\(\Rightarrow\)-8x+6y=x+2y
\(\Rightarrow\)6y-2y=x+8x \(\Rightarrow\)4y=9x
\(\Rightarrow\frac{x}{y}=\frac{4}{9}\)
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