Question

how do I simplify ((3x+2y)(x-2y)/x^2)/(2y-x)^2/x^3y

Answer 1

Please help!
\[\frac{ (3x + 2y)(x - 2y) }{ x ^{2} }\div \frac{ (2y-x)^{2} }{ x ^{3}y }\]

Answer 2

\[(2 y-x)^2=(x-2 y)^2 \]Proof:\[(2 y-x)^2=x^2-4 x y+4 y^2 \]\[(x-2 y)^2=x^2-4 x y+4 y^2 \]Change the numerator of the problem's divisor, (2y-x)^2 to (x-2y)^2 and then simplify. Verify that the final result is:\[\frac{x y (3 x+2 y)}{x-2 y} \]