165 Вправа 165Алгебра 8 клас Бевз 2025 · § 4 · стор. 37

165. Виконай віднімання дробів.

а) ${\displaystyle \frac{{a+3}^{\mathrm{\setminus }4}}{a}-\frac{7}{4a}=}$${\displaystyle \frac{4(a+3)-7}{4a}=}$${\displaystyle \frac{4a+12-7}{4a}=}$${\displaystyle \frac{4a+5}{4a}}$;

б) ${\displaystyle \frac{{x+5y}^{\mathrm{\setminus }x}}{y}-\frac{{y+5x}^{\mathrm{\setminus }y}}{x}=}$${\displaystyle \frac{x(x+5y)-y(y+5x)}{xy}}$=

=${\displaystyle \frac{x^2+5xy-5xy-y^2}{xy}=}$${\displaystyle \frac{x^2-y^2}{xy}=}$${\displaystyle \frac{\left(x-y\right)\left(x+y\right)}{xy}}$;

в) ${\displaystyle \frac{a^{\mathrm{\setminus }a}}{a+b}-\frac{b^2}{a(a+b)}=}$${\displaystyle \frac{a^2-b^2}{a(a+b)}=}$${\displaystyle \frac{(a-b)\cancel{\left(a+b\right)}}{a\cancel{\left(a+b\right)}}=}$${\displaystyle \frac{a-b}{a}}$.