404 Вправа 404Алгебра 8 клас Тарасенкова 2025 · § 10 · стор. 112

404. Спростіть вираз:

1) ${\displaystyle \frac{a^2}{a+3}-9{(a+3)}^{-1}=}$${\displaystyle \frac{a^2-9}{a+3}=}$${\displaystyle \frac{(a-3)\cancel{\left(a+3\right)}}{\cancel{a+3}}=}$${\displaystyle a-3}$;

2) ${\displaystyle \frac{p}{m-p}-m{(m-p)}^{-1}=}$${\displaystyle \frac{p-m}{m-p}=}$${\displaystyle \frac{-\cancel{\left(m-p\right)}}{\cancel{m-p}}=}$${\displaystyle -1}$;

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

4) ${\displaystyle \frac{1}{m-p}+p{(m-p)}^{-2}=}$${\displaystyle \frac{1^{\mathrm{\setminus }m-p}}{m-p}+\frac{p}{{(m-p)}^2}=}$${\displaystyle \frac{1\cdot \left(m-p\right)}{{(m-p)}^2}+\frac{p}{{(m-p)}^2}=}$${\displaystyle \frac{\left(m-p\right)+p}{{(m-p)}^2}=}$${\displaystyle \frac{m\cancel{-p}\cancel{+p}}{{(m-p)}^2}=}$${\displaystyle \frac{m}{{\left(m-p\right)}^2}}$.