Express in simplest terms: (4x/y^2 - 1/x) / (1/x + 2/y)show step by step solution to explain the answer

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`((4x)/y^2 - 1/x) / (1/x + 2/y)`

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`=((4x^2-y^2)/(y^2x)) / ((y+2x)/(yx)) `

This gives,

`= 1/y[(4x^2-y^2)/(2x+y)]`

`= 1/y[((2x+y)(2x-y))/(2x+y)]`

This simplifies into,

`= 1/y(2x-y)`

Therefore,

`((4x)/y^2 - 1/x) / (1/x + 2/y) = (2x-y)/y`

 

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