825 Вправа 825Алгебра 8 клас Тарасенкова 2025 · § 20 · стор. 244

825. Спростіть вираз (7/(5х² + 3х − 2) − 5/(5х − 2))·(х² + 2х + 1)/(х² + 3х + 2).

${\displaystyle 5x^2+3x-2=}$${\displaystyle (5x-2)(x+1)}$; ${\displaystyle x^2+3x+2=}$${\displaystyle (x+1)(x+2)}$;

${\displaystyle (\frac{7}{5x^2+3x-2}-\frac{5}{5x-2})\cdot \frac{x^2+2x+1}{x^2+3x+2}=}$${\displaystyle (\frac{7}{(5x-2)(x+1)}-\frac{5^{\mathrm{\setminus }x+1}}{5x-2})\cdot \frac{(x+1)(x+1)}{(x+1)(x+2)}=}$${\displaystyle \frac{7-5(x+1)}{(5x-2)(x+1)}\cdot \frac{\cancel{\left(x+1\right)}(x+1)}{\cancel{\left(x+1\right)}(x+2)}=}$${\displaystyle \frac{7-5x-5}{(5x-2)(x+1)}\cdot \frac{x+1}{x+2}=}$${\displaystyle \frac{2-5x}{(5x-2)\cancel{\left(x+1\right)}}\cdot \frac{\cancel{\left(x+1\right)}}{x+2}=}$${\displaystyle \frac{-\cancel{\left(5x-2\right)}}{\cancel{\left(5x-2\right)}(x+2)}=}$${\displaystyle -\frac{1}{x+2}}$.