155 Вправа 155Алгебра 8 клас Бевз 2025 · § 4 · стор. 36

155. Доведи тотожність.

а) ${\displaystyle \frac{m}{m-n}-\frac{n}{m-n}=}$${\displaystyle \frac{\cancel{\left(m-n\right)}}{\cancel{\left(m-n\right)}}=}$${\displaystyle 1}$;

${\displaystyle 1=}$${\displaystyle 1}$ — тотожність доведено;

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

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

${\displaystyle 1=}$${\displaystyle 1}$ — тотожність доведено;

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

${\displaystyle 1=}$${\displaystyle 1}$ — тотожність доведено;

г) ${\displaystyle \frac{x(1-y)}{x-y}-\frac{y(1-x)}{x-y}=}$${\displaystyle \frac{x(1-y)-y(1-x)}{x-y}}$=

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

${\displaystyle 1=}$${\displaystyle 1}$ — тотожність доведено.