([latex] \frac{2y}{x} - \frac{x}{2y} [/latex]):(2y-x) ,если x= [latex] \frac{1}{9} [/latex] y= [latex] \frac{1}{6} [/latex]

Question

([latex] \frac{2y}{x} - \frac{x}{2y} [/latex]):(2y-x) ,если x= [latex] \frac{1}{9} [/latex] y= [latex] \frac{1}{6} [/latex]

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Accepted Answer

[latex](\frac{2y}{x}-\frac{x}{2y}):(2y-x)=\frac{4y^2-x^2}{2xy}\cdot \frac{1}{2y-x}=\frac{(2y-x)(2y+x)}{2xy(2y-x)}=\\\\=\frac{2y+x}{2xy}=\frac{\frac{2}{6}+\frac{1}{9}}{\frac{2}{6\cdot 9}}=\frac{\frac{4}{9}}{\frac{1}{27}}=12[/latex]