172 Вправа 172Алгебра 8 клас Тарасенкова 2025 · § 4 · стор. 51

172. Виконайте дії:

1) ${\displaystyle x^2-6x+8=}$${\displaystyle x^2-2x-4x+8=}$${\displaystyle (x-2)(x-4)}$;

${\displaystyle \frac{x^2-4}{(x-2)(x-4)}=}$${\displaystyle \frac{\cancel{\left(x-2\right)}(x+2)}{\cancel{\left(x-2\right)}(x-4)}=}$${\displaystyle \frac{x+2}{x-4}}$;

${\displaystyle \frac{x}{x-4}-\frac{x+2}{x-4}=}$${\displaystyle \frac{x-x-2}{x-4}=}$${\displaystyle -\frac{2}{x-4}}$;

2) ${\displaystyle 2x^2-7x-4=}$${\displaystyle 2x^2-8x+x-4=}$${\displaystyle (x-4)(2x+1)}$;

${\displaystyle \frac{x\cdot \left(x-4\right)+6\cdot \left(2x+1\right)-(8x+6)}{(x-4)(2x+1)}=}$${\displaystyle \frac{x^2-4x+12x+6-8x-6}{(x-4)(2x+1)}=}$${\displaystyle \frac{x^2}{\left(x-4\right)\left(2x+1\right)}}$.