Question

упростите выражение

2mn/m^3+n^3+2m/m^2-n^2-1/m-n

Answer 1

$displaystyle frac{2mn}{m^3+n^3}+ frac{2m}{m^2-n^2}- frac{1}{m-n}$

1) действие

$displaystyle frac{2mn}{(m+n)(m^2-mn+n^2)}+ frac{2m}{(m-n)(m+n)}=\ =frac{2mn(m-n)+2m(m^2-mn+n^2)}{(m-n)(m+n)(m^2-mn+n^2)}=\= frac{2m^2n-2mn^2+2m^3-2m^2n+2mn^2}{(m-n)(m+n)m^2-mn+n^2)}=\= frac{2m^3}{(m-n)(m+n)(m^2-mn+b^2)}$

2) действие

$displaystyle frac{2m^3}{(m-n)(m+n)(m^2-mn+n^2)}- frac{1}{(m-n)}=\= frac{2m^3-1(m+n)(m^2-mn+n^2)}{(m-n)(m+n)(m^2-mn+n^2)}=\= frac{2m^3-(m^3+n^3)}{(m-n)(m+n)(m^2-mn+n^2)}= frac{m^3-n^3}{(m-n)(m+n)(m^2-mn+n^2)}\= frac{(m-n)(m^2+mn+n^2)}{(m-n)(m+n)(m^2-mn+n^2)}=\= frac{m^2+mn+n^2}{m^3+n^3}$