[tex]\frac{m ^{2}+mn-n ^{2} }{m ^{2}+2mn+n ^{2} }+ \frac{m ^{2}+mn+n ^{2} } {m^2+2mn+n ^{2} }\\ \\m\neq n\\\\ \frac{m ^{2}+mn-n ^{2} }{m ^{2}+2mn+n ^{2} }+ \frac{m ^{2}+mn+n ^{2} }{m ^{2}+2mn+n ^{2} }=\frac{m ^{2}+mn-n ^{2}+m ^{2}+mn+n ^{2} }{m ^{2}+2mn+n ^{2} } =\\\\=\frac{2m ^{2}+2mn }{(m +n )^{2} } =\frac{2m (m + n ) }{(m +n )^{2} }= \frac{2m }{ m +n }[/tex]
