178 Вправа 178Алгебра 8 клас Бевз 2025 · § 4 · стор. 38

178. Спрости вираз.

а) ${\displaystyle \frac{3x+y}{x-y}+\frac{4y}{y-x}=}$${\displaystyle \frac{3x+y}{x-y}-\frac{4y}{x-y}=}$${\displaystyle \frac{3x+y-4y}{x-y}}$=

=${\displaystyle \frac{3x-3y}{x-y}=}$${\displaystyle \frac{3\cancel{\left(x-y\right)}}{\cancel{\left(x-y\right)}}=}$${\displaystyle 3}$;

б) ${\displaystyle \frac{3a}{a-5}-\frac{a-20}{5-a}=}$${\displaystyle \frac{3a}{a-5}+\frac{a-20}{a-5}=}$${\displaystyle \frac{3a+a-20}{a-5}}$=

=${\displaystyle \frac{4a-20}{a-5}=}$${\displaystyle \frac{4\cancel{\left(a-5\right)}}{\cancel{\left(a-5\right)}}=}$${\displaystyle 4}$;

в) ${\displaystyle \frac{m^2}{m-4}+\frac{8m-16}{4-m}=}$${\displaystyle \frac{m^2}{m-4}-\frac{8m-16}{m-4}=}$${\displaystyle \frac{m^2-(8m-16)}{m-4}}$=

=${\displaystyle \frac{m^2-8m+16}{m-4}=}$${\displaystyle \frac{(m-4)\cancel{\left(m-4\right)}}{\cancel{\left(m-4\right)}}=}$${\displaystyle m-4}$;

г) ${\displaystyle \frac{2a-1}{9a^2-1}-\frac{a+2}{1-9a^2}=}$${\displaystyle \frac{2a-1}{(3a-1)(3a+1)}+\frac{a+2}{(3a-1)(3a+1)}}$=

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