Question

C^2/(c-5)^2* 25-c^2/5c+25 + c/c-5=-(c/5)
Докажите тождество

Answer 1

$frac{c^2}{(c-5)^2} * frac{25-c^2}{5c+25}+ frac{c}{c-5}= frac{c^2}{(c-5)^2} * frac{-(c-5)(c+5)}{5(c+5)}+ frac{c}{c-5}= frac{c^2}{(c-5)} * frac{-1}{5}+ frac{c}{c-5}= \ \ = frac{-c^2}{5(c-5)} + frac{c}{c-5}= frac{-c^2+5c}{5(c-5)}=frac{-c(c-5)}{5(c-5)}= - frac{c}{5}$