Simplify $\frac{2 x}{2 x - y} - \frac{y}{2 x + y} - \frac{4 x y}{4 x^{2} - y^{2}}$ $(2x)/(2x-y) - y/(2x+y) - (4xy)/(4x^2-y^2)$ ?

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Simplify $\frac{2 x}{2 x - y} - \frac{y}{2 x + y} - \frac{4 x y}{4 x^{2} - y^{2}}$ $(2x)/(2x-y) - y/(2x+y) - (4xy)/(4x^2-y^2)$ ?

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Answer 1 · 2016-12-06T02:52:18

$\frac{2 x - y}{2 x + y}$ $(2x-y)/(2x+y)$ Where $y \neq 2 x$ $y!=2x$

Explanation:

First consider the first two terms:

$\frac{2 x}{2 x - y} - \frac{y}{2 x + y} = \frac{2 x (2 x + y) - y (2 x - y)}{4 x^{2} - y^{2}}$ $(2x)/(2x-y) - y/(2x+y) = (2x(2x+y) - y(2x-y))/ (4x^2-y^2)$

Now combine this result with the third term:

$\frac{2 x (2 x + y) - y (2 x - y)}{4 x^{2} - y^{2}} - \frac{4 x y}{4 x^{2} - y^{2}}$ $(2x(2x+y) - y(2x-y))/ (4x^2-y^2) - (4xy)/(4x^2-y^2)$

$= \frac{4 x^{2} + 2 x y - 2 x y + y^{2} - 4 x y}{4 x^{2} - y^{2}}$ $= (4x^2+2xy-2xy+y^2 -4xy)/(4x^2-y^2)$

$= \frac{4 x^{2} + y^{2} - 4 x y}{4 x^{2} - y^{2}}$ $= (4x^2+y^2 -4xy)/(4x^2-y^2)$

Factorise top and bottom:

$= \frac{(2 x - y) (2 x - y)}{(2 x + y) (2 x - y)}$ $=((2x-y)(2x-y))/((2x+y)(2x-y))$

$=(cancel((2x-y))(2x-y))/((2x+y)*cancel((2x-y)))$ Where $2x-y !=0$

$=(2x-y)/(2x+y)$ Where $y!=2x$

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Simplify $\frac{2 x}{2 x - y} - \frac{y}{2 x + y} - \frac{4 x y}{4 x^{2} - y^{2}}$ $(2x)/(2x-y) - y/(2x+y) - (4xy)/(4x^2-y^2)$ ?

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Explanation:

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Simplify (2x)/(2x-y) - y/(2x+y) - (4xy)/(4x^2-y^2)2x2x−y−y2x+y−4xy4x2−y2(2x)/(2x-y) - y/(2x+y) - (4xy)/(4x^2-y^2) ?

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Explanation:

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Simplify $\frac{2 x}{2 x - y} - \frac{y}{2 x + y} - \frac{4 x y}{4 x^{2} - y^{2}}$ $(2x)/(2x-y) - y/(2x+y) - (4xy)/(4x^2-y^2)$ ?