70 Вправа 70Алгебра 8 клас Бевз 2025 · § 2 · стор. 20

70. Зведи до спільного знаменника дроби.

а) ${\displaystyle \frac{2}{x}}$ і ${\displaystyle \frac{1}{a}}$; спільний знаменник ${\displaystyle ax}$;

${\displaystyle \frac{2}{x}=}$${\displaystyle \frac{2\cdot a}{x\cdot a}=}$${\displaystyle \frac{2a}{ax}}$;

${\displaystyle \frac{1}{a}=}$${\displaystyle \frac{1\cdot x}{a\cdot x}=}$${\displaystyle \frac{x}{ax}}$;

б) ${\displaystyle \frac{a}{2m}}$ і ${\displaystyle \frac{b}{3m^2}}$; спільний знаменник ${\displaystyle 6m^2}$;

${\displaystyle \frac{a}{2m}=}$${\displaystyle \frac{a\cdot 3m}{2m\cdot 3m}=}$${\displaystyle \frac{3am}{6m^2}}$;

${\displaystyle \frac{b}{3m^2}=}$${\displaystyle \frac{b\cdot 2}{3m^2\cdot 2}=}$${\displaystyle \frac{2b}{6m^2}}$;

в) ${\displaystyle \frac{2}{c}}$ і ${\displaystyle \frac{1}{a-b}}$; спільний знаменник ${\displaystyle c(a-b)}$;

${\displaystyle \frac{2}{c}=}$${\displaystyle \frac{2\cdot \left(a-b\right)}{c\cdot \left(a-b\right)}=}$${\displaystyle \frac{2\left(a-b\right)}{c\left(a-b\right)}}$;

${\displaystyle \frac{1}{a-b}=}$${\displaystyle \frac{1\cdot c}{(a-b)\cdot c}=}$${\displaystyle \frac{c}{c\left(a-b\right)}}$;

г) ${\displaystyle \frac{8}{x}}$ і ${\displaystyle \frac{7}{x(x-a)}}$; спільний знаменник ${\displaystyle x(x-a)}$;

${\displaystyle \frac{8}{x}=}$${\displaystyle \frac{8\cdot \left(x-a\right)}{x\cdot \left(x-a\right)}=}$${\displaystyle \frac{8\left(x-a\right)}{x\left(x-a\right)}}$;

${\displaystyle \frac{7}{x(x-a)}=}$${\displaystyle \frac{7}{x\left(x-a\right)}}$;

ґ) ${\displaystyle \frac{1}{x-a}}$ і ${\displaystyle \frac{1}{x+a}}$; спільний знаменник ${\displaystyle (x-a)(x+a)}$;

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

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

д) ${\displaystyle \frac{1}{{(a+b)}^2}}$ і ${\displaystyle \frac{2a}{a+b}}$; спільний знаменник ${\displaystyle {(a+b)}^2}$;

${\displaystyle \frac{1}{{(a+b)}^2}=}$${\displaystyle \frac{1}{{\left(a+b\right)}^2}}$;

${\displaystyle \frac{2a}{a+b}=}$${\displaystyle \frac{2a\cdot \left(a+b\right)}{(a+b)\cdot \left(a+b\right)}=}$${\displaystyle \frac{2a\left(a+b\right)}{{\left(a+b\right)}^2}}$.