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Express in simplest terms: `((4x)/y^2 - 1/x) / (1/x + 2/y)`

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spock15 | Student, Undergraduate | eNoter

Posted May 26, 2012 at 7:59 PM via web

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Express in simplest terms: `((4x)/y^2 - 1/x) / (1/x + 2/y)`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 26, 2012 at 8:06 PM (Answer #1)

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The expression `((4x)/y^2 - 1/x) / (1/x + 2/y)` has to be simplified.

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

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

=> `(((2x - y)(2x + y))/(y^2*x))/((y + 2x)/(x*y))`

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

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

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newtoncarlos | Middle School Teacher | eNoter

Posted May 26, 2012 at 9:05 PM (Answer #2)

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To simplify (4x/y^2-1/x)/(1/x+2/y)

multiply each terms by their LCD. (LCD=xy^2)

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

=(4x^2-y^2)/(y^2+2xy)

removing the common factor

=(2x+y)(2x-y)/y(y+2x)

=(2x-y)/y

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