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Combine all terms into a single fraction with $2y$ as common denominator
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$\frac{d}{dx}\left(\frac{x-y}{\frac{y-x}{2y}\left(\sqrt{x-y}-\sqrt{x+y}\right)}\right)$
Learn how to solve problems step by step online. Simplify the expression (x-y)/((1/2+(-x)/(2y))((x-y)^1/2-(x+y)^1/2)). Combine all terms into a single fraction with 2y as common denominator. Multiplying the fraction by \sqrt{x-y}-\sqrt{x+y}. Divide fractions \frac{x-y}{\frac{\left(y-x\right)\left(\sqrt{x-y}-\sqrt{x+y}\right)}{2y}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Simplify \frac{2\left(x-y\right)y}{\left(y-x\right)\left(\sqrt{x-y}-\sqrt{x+y}\right)} multiplying the denominator by -1.