229 Вправа 229Алгебра 8 клас Тарасенкова 2025 · § 6 · стор. 66

229. Спростіть вираз.

1) ${\displaystyle \frac{16a^2{b}^2}{5xy}\cdot \frac{25x^2{y}^3}{12a{b}^3}\cdot \frac{3a^2}{4y}=}$${\displaystyle \frac{1200a^4{b}^2{x}^2{y}^3}{240a{b}^{3}x{y}^2}=}$${\displaystyle \frac{\cancel{240a{b}^{2}x{y}^2}\cdot 5a^{3}xy}{\cancel{240a{b}^{2}x{y}^2}\cdot b}=}$${\displaystyle \frac{5a^{3}xy}{b}}$;

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