196° Вправа 196Алгебра 8 клас Тарасенкова 2025 · § 5 · стор. 58

196. Скоротіть дріб і піднесіть до степеня.

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

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

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