164 Вправа 164Алгебра 8 клас Бевз 2025 · § 4 · стор. 37

164. Find the difference of the fractions.

a) ${\displaystyle \frac{3^{\mathrm{\setminus }a+b}}{a-b}-\frac{2^{\mathrm{\setminus }a-b}}{a+b}=}$${\displaystyle \frac{3(a+b)-2(a-b)}{(a-b)(a+b)}}$=

=${\displaystyle \frac{3a+3b-2a+2b}{(a-b)(a+b)}=}$${\displaystyle \frac{a+5b}{(a-b)(a+b)}=}$${\displaystyle \frac{a+5b}{a^2-b^2}}$;

b) ${\displaystyle \frac{x^2}{{(a+x)}^2}-\frac{x}{a+x}=}$${\displaystyle \frac{x^2}{{(x+a)}^2}-\frac{x^{\mathrm{\setminus }x+a}}{x+a}=}$${\displaystyle \frac{x^2-x(x+a)}{{(x+a)}^2}}$=

=${\displaystyle \frac{x^2-ax-x^2}{{(x+a)}^2}=}$${\displaystyle \frac{-xa}{{\left(x+a\right)}^2}}$;

c) ${\displaystyle \frac{x^{\mathrm{\setminus }5c^2}}{3a^2{b}^{3}c}-\frac{2^{\mathrm{\setminus }3a{b}^2}}{5ab{c}^3}=}$${\displaystyle \frac{5x{c}^2-6a{b}^2}{15a^2{b}^3{c}^3}}$.