Question

$frac{m-2}{6-m} - frac{m-3}{m+6} + frac{2m(m-2)}{(m+6)(m-6)}$ Решите пож)

Answer 1

$frac{m-2}{6-m}-frac{m-3}{m+6}+frac{2m(m-2)}{(m+6)(m-6)}=frac{2-m}{m-6}-frac{m-3}{m+6}+frac{2m(m-2)}{(m+6)(m-6)}=\ =frac{(2-m)(m+6)-(m-3)(m-6)+2m(m-2)}{(m+6)(m-6)}=\ =frac{2m+12-m^2-6m-(m^2-6m-3m+18)+2m^2-4m}{(m+6)(m-6)}=\ =frac{-m^2-4m+12-m^2+9m-18+2m^2-4m}{(m+6)(m-6)}=\ = frac{m-6}{(m+6)(m-6)}=frac{1}{m+6}$