85 Вправа 85Алгебра 8 клас Бевз 2025 · § 2 · стор. 22

85. Спрости вираз.

а) ${\displaystyle \frac{3x+2+3xy+2y}{2y-2+3xy-3x}}$;

${\displaystyle \frac{(3x+2)+y(3x+2)}{2(y-1)+3x(y-1)}=}$${\displaystyle \frac{\cancel{\left(3x+2\right)}(1+y)}{(y-1)\cancel{\left(2+3x\right)}}=}$${\displaystyle \frac{y+1}{y-1}}$;

б) ${\displaystyle \frac{(x+2)(x-1)}{x^3+2x^2-x-2}}$;

${\displaystyle \frac{(x+2)(x-1)}{x^2(x+2)-(x+2)}=}$${\displaystyle \frac{(x+2)(x-1)}{(x+2)(x^2-1)}}$=

=${\displaystyle \frac{\cancel{\left(x+2\right)}\cancel{\left(x-1\right)}}{\cancel{\left(x+2\right)}\cancel{\left(x-1\right)}(x+1)}=}$${\displaystyle \frac{1}{x+1}}$;

в) ${\displaystyle \frac{x^2-4x+3}{x^2-2x-3}}$;

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