152 Вправа 152Алгебра 8 клас Бевз 2025 · § 4 · стор. 36

152. Подай у вигляді дробу або одночлена вираз.

а) ${\displaystyle \frac{2}{3a}+\frac{4}{3a}-\frac{6-a^2}{3a}=}$${\displaystyle \frac{2+4-(6-a^2)}{3a}=}$${\displaystyle \frac{2+4-6+a^2}{3a}}$=

=${\displaystyle \frac{a^2}{3a}=}$${\displaystyle \frac{a\cancel{a}}{3\cancel{a}}=}$${\displaystyle \frac{a}{3}}$;

б) ${\displaystyle \frac{2a+3}{5b}+\frac{2a-9}{5b}+\frac{a+1}{5b}=}$${\displaystyle \frac{2a+3+2a-9+a+1}{5b}}$=

=${\displaystyle \frac{5a-5}{5b}=}$${\displaystyle \frac{(a-1)\cancel{5}}{b\cancel{5}}=}$${\displaystyle \frac{a-1}{b}}$;

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

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

г) ${\displaystyle \frac{2(m-n)}{m-n}-\frac{m}{m-n}+\frac{n}{m-n}=}$${\displaystyle \frac{2m-2n-m+n}{m-n}=}$${\displaystyle \frac{\cancel{\left(m-n\right)}}{\cancel{\left(m-n\right)}}=}$${\displaystyle 1}$.