Question

Упростите выражение и найдите его значение !!!

Answer 1

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

Answer 2

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

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