274 Вправа 274Алгебра 8 клас Бевз 2025 · § 6 · стор. 58

274. НМТ. Спрости вираз.

а) ${\displaystyle \frac{x^2-4xy+4y^2}{x-2y}:(2y-x)=}$${\displaystyle \frac{x^2-4xy+4y^2}{x-2y}\cdot \frac{1}{2y-x}}$=

=${\displaystyle \frac{x^2-4xy+4y^2}{(x-2y)\cdot (2y-x)}=}$${\displaystyle -\frac{\cancel{{\left(x-2y\right)}^2}}{\cancel{{\left(x-2y\right)}^2}}=}$${\displaystyle -1}$;

б) ${\displaystyle \frac{x^2-y^2}{x-y}:(2x+2y)=}$${\displaystyle \frac{x^2-y^2}{x-y}\cdot \frac{1}{2x+2y}}$=

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