146 Вправа 146Алгебра 8 клас Бевз 2025 · § 4 · стор. 35

146. Знайди різницю дробів.

а) ${\displaystyle \frac{2c}{3ax}-\frac{c}{3ax}=}$${\displaystyle \frac{2c-c}{3ax}=}$${\displaystyle \frac{c}{3ax}}$;

б) ${\displaystyle \frac{7x}{6ab}-\frac{x}{6ab}=}$${\displaystyle \frac{7x-x}{6ab}=}$${\displaystyle \frac{x\cancel{6}}{ab\cancel{6}}=}$${\displaystyle \frac{x}{ab}}$;

в) ${\displaystyle \frac{2a}{a-3}-\frac{6}{a-3}=}$${\displaystyle \frac{2a-6}{a-3}=}$${\displaystyle \frac{2\cancel{\left(a-3\right)}}{\cancel{\left(a-3\right)}}=}$${\displaystyle 2}$;

г) ${\displaystyle \frac{4x+1}{3x-2}-\frac{x+3}{3x-2}=}$${\displaystyle \frac{4x+1-(x+3)}{3x-2}=}$${\displaystyle \frac{4x+1-x-3}{3x-2}}$=

=${\displaystyle \frac{\cancel{\left(3x-2\right)}}{\cancel{\left(3x-2\right)}}=}$${\displaystyle 1}$;

ґ) ${\displaystyle \frac{a^2}{a-c}-\frac{c^2}{a-c}=}$${\displaystyle \frac{a^2-c^2}{a-c}=}$${\displaystyle \frac{(a+c)\cancel{\left(a-c\right)}}{\cancel{\left(a-c\right)}}=}$${\displaystyle a+c}$;

д) ${\displaystyle \frac{x^2+1}{{(x-1)}^2}-\frac{2x}{{(x-1)}^2}=}$${\displaystyle \frac{x^2+1-2x}{{(x-1)}^2}=}$${\displaystyle \frac{\cancel{{\left(x-1\right)}^2}}{\cancel{{\left(x-1\right)}^2}}=}$${\displaystyle 1}$.