465 Вправа 465Алгебра 8 клас Бевз 2025 · § 9 · стор. 93

465. Спрости вираз.

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

б) ${\displaystyle \frac{a^{-2}-4}{a^{-2}+4a^{-1}+4}=}$${\displaystyle \frac{(a^{-1}-2)(a^{-1}+2)}{{(a^{-1}+2)}^2}}$=

=${\displaystyle \frac{a^{-1}-2}{a^{-1}+2}=}$${\displaystyle \frac{1-2a}{1+2a}}$;

в) ${\displaystyle \frac{a^8+a^{12}}{a^{-8}+a^{-12}}=}$${\displaystyle \frac{a^8(1+a^4)}{a^{-12}(a^4+1)}=}$${\displaystyle a^{20}}$;

г) ${\displaystyle \frac{x^4+3x^5+x^6}{x^{-4}+3x^{-5}+x^{-6}}=}$${\displaystyle \frac{x^4(1+3x+x^2)}{x^{-6}(x^2+3x+1)}=}$${\displaystyle x^{10}}$.