Question

Выполните сложение дробей , если y неравен 7 $frac{7}{7-y} - frac{7-y}{y}$

Answer 1

$frac{7}{7-y}-frac{7-y}{7}=frac{7*7}{(7-y)7}-frac{(7-y)(7-y)}{7(7-y)}= frac{49-(7-y)^2}{7(7-y)}=frac{49-(49-14y+y^2)}{7(7-y)}= \ \ \ = frac{49-49+14y-y^2}{7(7-y)}=frac{14y-y^2}{7(7-y)}=frac{y(14-y)}{7(7-y)}$