Question

Помогите пож-та даю 34 балла

Answer 1

$displaystyle a)..(frac{2x-y}{2x+y}-frac{4x^{2}+y^{2}}{4x^{2}-y^{2}})*(frac{1}{2x}+frac{1}{y})=\\=(frac{2x-y}{2x+y}-frac{4x^{2}+y^{2}}{(2x-y)(2x+y)})*(frac{2x+y}{2xy})=\\=frac{(2x-y)^{2} -4x^{2}-y^{2} }{(2x-y)(2x+y)}*(frac{2x+y}{2xy})=\\=frac{4x^{2}-4xy+y^{2}-4x^{2}-y^{2}}{2xy(2x-y)}= -frac{4xy}{2xy(2x-y)}=frac{2}{y-2x};\\\b)..frac{m-n}{m}:(frac{m}{n}+ frac{n}{m}-2)=frac{m-n}{m}:(frac{m^{2}+n^{2}-2mn}{mn})=\\=frac{m-n}{m}*frac{mn}{(m-n)^{2}}= frac{n}{m-n};$

$displaystyle c)..(1- frac{a}{b})*( frac{a}{a-b}- frac{b}{a+b}+ frac{2ab}{a^{2}-b^{2}})= \ \=-frac{a-b}{b}* frac{a(a+b)-b(a-b)+2ab}{(a-b)(a+b)}=- frac{a^{2}+ab+b^{2}-ab+2ab}{b(a+b)}= \ \ =- frac{(a+b)^{2} }{b(a+b)}= -frac{a+b}{b};$