Question

Задание сложение алгебраических дробей

Answer 1

$\frac{4c+3y}{c^2-y^2}- \frac{3}{c-y}=\frac{4c+3y}{(c-y) \cdot (c+y)}- \frac{3}{c-y}=\frac{4c+3y-3c-3y}{(c-y)\cdot (c+y)}=\frac{c}{(c-y)\cdot (c+y)} \\ \\ \\ \frac{c}{(c-y)\cdot (c+y)} + \frac{1}{y-c}=\frac{c}{(c-y)\cdot (c+y)} - \frac{1}{c-y}=\frac{c-c-y}{(c-y)\cdot (c+y)}=-\frac{y}{(c-y)\cdot (c+y)} \\ \\ \\ -\frac{y}{(c-y) (c+y)} - \frac{4}{5y+5c}=\frac{-y}{(c-y) (c+y)} - \frac{4}{5(y+c)}=\frac{-5y-4c+4y}{(c-y)(c+y)}=\frac{-y-4c}{5(c-y) (c+y)}}=\\ \\=-\frac{4c+y}{5(c^2-y^2)}=\frac{4c+y}{5(y^2-c^2)}$