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[latex]\displaystyle a)..(\frac{2x-y}{2x+y}-\frac{4x^{2}+y^{2}}{4x^{2}-y^{2}})*(\frac{1}{2x}+\frac{1}{y})=\\\\=(\frac{2x-y}{2x+y}-\frac{4x^{2}+y^{2}}{(2x-y)(2x+y)})*(\frac{2x+y}{2xy})=\\\\=\frac{(2x-y)^{2} -4x^{2}-y^{2} }{(2x-y)(2x+y)}*(\frac{2x+y}{2xy})=\\\\=\frac{4x^{2}-4xy+y^{2}-4x^{2}-y^{2}}{2xy(2x-y)}= -\frac{4xy}{2xy(2x-y)}=\frac{2}{y-2x};\\\\\\b)..\frac{m-n}{m}:(\frac{m}{n}+ \frac{n}{m}-2)=\frac{m-n}{m}:(\frac{m^{2}+n^{2}-2mn}{mn})=\\\\=\frac{m-n}{m}*\frac{mn}{(m-n)^{2}}= \frac{n}{m-n}; \\ [/latex]
[latex]\displaystyle c)..(1- \frac{a}{b})*( \frac{a}{a-b}- \frac{b}{a+b}+ \frac{2ab}{a^{2}-b^{2}})= \\ \\=-\frac{a-b}{b}* \frac{a(a+b)-b(a-b)+2ab}{(a-b)(a+b)}=- \frac{a^{2}+ab+b^{2}-ab+2ab}{b(a+b)}= \\ \\ =- \frac{(a+b)^{2} }{b(a+b)}= -\frac{a+b}{b}; [/latex]
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