464 Вправа 464Алгебра 8 клас Бевз 2025 · § 9 · стор. 93

464. Спрости вираз.

а) ${\displaystyle \frac{a^{-2}-4}{a^{-1}+2}=}$${\displaystyle \frac{(a^{-1}-2)\cancel{\left(a^{-1}+2\right)}}{\cancel{a^{-1}+2}}=}$${\displaystyle a^{-1}-2}$;

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

=${\displaystyle \frac{x^{-1}-1}{x^{-1}+1}=}$${\displaystyle \frac{1-x}{1+x}}$;

в) ${\displaystyle \frac{x^7+x^{13}}{x^{-3}+x^3}=}$${\displaystyle \frac{x^7\cancel{\left(1+x^6\right)}}{x^{-3}\cancel{\left(1+x^6\right)}}=}$${\displaystyle x^{10}}$;

г) ${\displaystyle \frac{x^4+2x^6+x^7}{2+x+x^{-2}}=}$${\displaystyle \frac{x^6(x^{-2}+2+x)}{2+x+x^{-2}}=}$${\displaystyle x^6}$.