157 Вправа 157Алгебра 8 клас Бевз 2025 · § 4 · стор. 36

157. Спрости вираз.

а) ${\displaystyle \frac{a^2}{a-4}-\frac{16}{a-4}=}$${\displaystyle \frac{a^2-16}{a-4}=}$${\displaystyle \frac{(a+4)\cancel{\left(a-4\right)}}{\cancel{\left(a-4\right)}}=}$${\displaystyle a+4}$;

б) ${\displaystyle \frac{3}{9-a^2}-\frac{a}{9-a^2}=}$${\displaystyle \frac{3}{(3-a)(a+3)}-\frac{a}{(3-a)(a+3)}}$=

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

в) ${\displaystyle \frac{a^2-2a}{a-9}+\frac{2a-81}{a-9}=}$${\displaystyle \frac{a^2-2a+2a-81}{a-9}=}$${\displaystyle \frac{a^2-81}{a-9}}$=

=${\displaystyle \frac{(a+9)\cancel{\left(a-9\right)}}{\cancel{\left(a-9\right)}}=}$${\displaystyle a+9}$.