86 Вправа 86Алгебра 8 клас Бевз 2025 · § 2 · стор. 22

86. Спрости вираз.

а) ${\displaystyle \frac{6a^2+15ab-8ac-20bc}{12a^2-9ab-16ac+12bc}}$;

${\displaystyle \frac{3a(2a+5b)-4c(2a+5b)}{3a(4a-3b)-4c(4a-3b)}=}$${\displaystyle \frac{(2a+5b)\cancel{\left(3a-4c\right)}}{(4a-3b)\cancel{\left(3a-4c\right)}}=}$${\displaystyle \frac{2a+5b}{4a-3b}}$;

б) ${\displaystyle \frac{2a^2-18}{a^2+2a-15}}$;

${\displaystyle \frac{2(a^2-9)}{a^2+5a-3a-15}=}$${\displaystyle \frac{2(a+3)\cancel{\left(a-3\right)}}{a(a+5)-3(a+5)}}$=

=${\displaystyle \frac{2(a+3)\cancel{\left(a-3\right)}}{(a+5)\cancel{\left(a-3\right)}}=}$${\displaystyle \frac{2\left(a+3\right)}{a+5}}$;

в) ${\displaystyle \frac{x{(y+1)}^2-y{(x+1)}^2}{x(y+1)-y(x+1)}}$;

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

=${\displaystyle \frac{\cancel{\left(x-y\right)}(1-xy)}{\cancel{x-y}}=}$${\displaystyle 1-xy}$.