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

### 2 Answers | Add Yours

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`

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

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes