Question

Упростите выражение и найдите его значение !!!

Answer 1

$(m- frac{4mn}{m+n} ):( frac{m}{n+m}+ frac{n}{m-n} + frac{2mn}{n^2-m^2} )= \ = frac{m^2+mn-4mn}{m+n} : frac{m(m-n)+n(m+n)-2mn}{m^2-n^2}} = \ = frac{m^2-3mn}{m+n} : frac{m^2-mn+mn+n^2-2mn}{m^2-n^2}} = frac{m^2-3mn}{m+n} : frac{(m-n)^2}{(m-n)(m+n)}} = \ frac{m(m-3n)(m-n)(m+n)}{(m+n)(m-n)^2} = frac{m(m-3n)}{m-n} =frac{0.2(0.2-3cdot(-0.8))}{0.2-(-0.8)} =0.52$

Answer 2

$(m- frac{4mn}{m+n}):( frac{m}{n+m} + frac{n}{m-n} + frac{2mn}{n^2-m^2} )= \\= frac{m(m+n)-4mn}{m+n} :( frac{m}{n+m} - frac{n}{n-m} + frac{2mn}{(n-m)(n+m)} )=\\= frac{m^2+mn-4mn}{m+n} : frac{m(n-m)-n(n+m)+2mn}{(n-m)(n+m)}=\\= frac{m^2-3mn}{m+n}: frac{mn-m^2-n^2-mn+2mn}{(n-m)(n+m)}= frac{m(m-3n)}{m+n}: frac{-(n^2-2mn+m^2)}{(n+m)(n-m)}=\\=-frac{m(m-3n)}{m+n}* frac{(n+m)(n-m)}{(n-m)^2}=- frac{m(m-3n)}{n-m}=\\=frac{m(m-3n)}{m-n}$

$m= frac{1}{5} , n=- frac{4}{5} \\ frac{ frac{1}{5}( frac{1}{5}-3(- frac{4}{5})) }{ frac{1}{5} - (-frac{4}{5}) } = frac{ frac{1}{5} ( frac{1}{5}+ frac{12}{5} )}{ frac{1}{5} + frac{4}{5} }= frac{ frac{1}{5}* frac{13}{5} }{1}= frac{13}{25}$