150 Вправа 150Алгебра 8 клас Бевз 2025 · § 4 · стор. 36

150. Подай у вигляді дробу або одночлена вираз.

а) ${\displaystyle \frac{1-a}{1-c^2}+\frac{a-3}{1-c^2}-\frac{c-3}{1-c^2}}$=

=${\displaystyle \frac{1-a}{(1-c)(c+1)}+\frac{a-3}{(1-c)(c+1)}-\frac{c-3}{(1-c)(c+1)}}$=

=${\displaystyle \frac{1-a+a-3-(c-3)}{(1-c)(c+1)}=}$${\displaystyle \frac{1-a+a-3-c+3}{(1-c)(c+1)}}$=

=${\displaystyle \frac{\cancel{\left(1-c\right)}}{(c+1)\cancel{\left(1-c\right)}}=}$${\displaystyle \frac{1}{c+1}}$;

б) ${\displaystyle \frac{a^2-c^3}{a-c}+\frac{c^3-a^3}{a-c}+\frac{a^3-c^2}{a-c}=}$${\displaystyle \frac{a^2-c^3+c^3-a^3+a^3-c^2}{a-c}}$=

=${\displaystyle \frac{a^2-c^2}{a-c}=}$${\displaystyle \frac{(a+c)\cancel{\left(a-c\right)}}{\cancel{\left(a-c\right)}}=}$${\displaystyle a+c}$.