163 Вправа 163Алгебра 8 клас Бевз 2025 · § 4 · стор. 37

163. Знайди різницю дробів.

а) ${\displaystyle \frac{4}{a{x}^2}-\frac{5^{\mathrm{\setminus }x}}{ax}=}$${\displaystyle \frac{4-5x}{a{x}^2}}$;

б) ${\displaystyle \frac{1}{c}-\frac{1}{a+c}=}$${\displaystyle \frac{1^{\mathrm{\setminus }c+a}}{c}-\frac{1^{\mathrm{\setminus }c}}{c+a}=}$${\displaystyle \frac{c+a-c}{c(c+a)}}$=

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

в) ${\displaystyle \frac{x^2-m}{m(x+m)}-\frac{x^{\mathrm{\setminus }x+m}}{m}=}$${\displaystyle \frac{x^2-m-x(x+m)}{m(x+m)}=}$${\displaystyle \frac{x^2-m-mx-x^2}{m(x+m)}}$=

=${\displaystyle \frac{-xm-m}{m(x+m)}=}$${\displaystyle \frac{(-(x+1))\cancel{m}}{(x+m)\cancel{m}}=}$${\displaystyle -\frac{x+1}{x+m}}$.