152° Вправа 152Алгебра 8 клас Тарасенкова 2025 · § 4 · стор. 48

152. Знайдіть різницю дробів.

1) ${\displaystyle \frac{1^{\mathrm{\setminus }2}}{4ab}-\frac{11}{8ab}=}$${\displaystyle \frac{1\cdot 2}{8ab}-\frac{11}{8ab}=}$${\displaystyle \frac{1\cdot 2-11}{8ab}=}$${\displaystyle -\frac{9}{8ab}}$;

2) ${\displaystyle \frac{{4y}^{\mathrm{\setminus }7}}{5ac}-\frac{22y}{35ac}=}$${\displaystyle \frac{4y\cdot 7}{35ac}-\frac{22y}{35ac}=}$${\displaystyle \frac{4y\cdot 7-22y}{35ac}=}$${\displaystyle \frac{28y-22y}{35ac}=}$${\displaystyle \frac{6y}{35ac}}$;

3) ${\displaystyle \frac{{13x}^{\mathrm{\setminus }5}}{15b^2}-\frac{{3x}^{\mathrm{\setminus }3}}{25b^2}=}$${\displaystyle \frac{13x\cdot 5}{75b^2}-\frac{3x\cdot 3}{75b^2}=}$${\displaystyle \frac{13x\cdot 5-3x\cdot 3}{75b^2}=}$${\displaystyle \frac{65x-9x}{75b^2}=}$${\displaystyle \frac{56x}{75b^2}}$;

4) ${\displaystyle \frac{{9a}^{\mathrm{\setminus }5}}{a-b}-\frac{4a}{5(a-b)}=}$${\displaystyle \frac{9a\cdot 5}{5(a-b)}-\frac{4a}{5(a-b)}=}$${\displaystyle \frac{9a\cdot 5-4a}{5(a-b)}=}$${\displaystyle \frac{41a}{5\left(a-b\right)}}$;

5) ${\displaystyle \frac{5c}{6(a+c)}-\frac{{12c}^{\mathrm{\setminus }6}}{a+c}=}$${\displaystyle \frac{5c}{6(a+c)}-\frac{12c\cdot 6}{6(a+c)}=}$${\displaystyle \frac{5c-12c\cdot 6}{6(a+c)}=}$${\displaystyle \frac{5c-72c}{6(a+c)}=}$${\displaystyle -\frac{67c}{6\left(a+c\right)}}$;

6) ${\displaystyle \frac{{9x}^{\mathrm{\setminus }5}}{8(a^2+1)}-\frac{x^{\mathrm{\setminus }2}}{20(a^2+1)}=}$${\displaystyle \frac{9x\cdot 5}{40(a^2+1)}-\frac{x\cdot 2}{40(a^2+1)}=}$${\displaystyle \frac{9x\cdot 5-x\cdot 2}{40(a^2+1)}=}$${\displaystyle \frac{43x}{40\left(a^2+1\right)}}$.