ПОВТОРЮЄМО АЛГЕБРУ ЗА 8 КЛАС: 18

18. Виконайте дію:

1) $\frac{3x(x-1)}{{9x}^2-y^2}$ + $\frac{\mathrm{xy}-y}{y^2-{9x}^2}$ = $\frac{3x(x-1)}{{9x}^2-y^2}$ – $\frac{\mathrm{xy}-y}{{9x}^2-y^2}$ = $\frac{{3x}^2-3x-\mathrm{xy}+y}{{9x}^2-y^2}$ = $\frac{3x(x-1)-y(x-1)}{(3x-y)(3x+y)}$ = $\frac{(3x-y)(x-1)}{(3x-y)(3x+y)}$ = $\frac{x-1}{3x+y}$.

2) $\frac{a-5}{{\mathrm{ab}-a}^2}$ – $\frac{5-b}{{\mathrm{ab}-b}^2}$ = $\frac{a-5}{a(b-a)}$ – $\frac{5-b}{b(a-b)}$ = $\frac{{5-a}^{\backslash b}}{a(a-b)}$ – $\frac{{5-b}^{\backslash a}}{b(a-b)}$ = $\frac{5b-\mathrm{ab}-5a+\mathrm{ab}}{\mathrm{ab}(a-b)}$ = $\frac{5b-5a}{\mathrm{ab}(a-b)}$ = $\frac{-5(a-b)}{\mathrm{ab}(a-b)}$ = –$\frac{5}{\mathrm{ab}}$;

3) $\frac{x^2+x-2}{x^2-4}$ – $\frac{2}{3x-6}$ – 1 = $\frac{x^2+x-2}{(x-2)(x+2)}$ – $\frac{2^{\backslash x+2}}{3(x-2)}$ – $1^{\backslash 3(x^2-4)}$ = $\frac{{3x}^2+3x-6-2x-4-{3x}^2+12}{3(x-2)(x+2)}$ = $\frac{x+2}{3(x-2)(x+2)}$ = $\frac{1}{3(x-2)}$ = $\frac{1}{3x-6}$;

4) $\frac{m^2-9}{a^2+6a+9}$ : $\frac{12-4m}{\mathrm{ap}+3p}$ = $\frac{(m-3)(m+3)}{{(a+3)}^2}$ • $\frac{p(a+3)}{4(3-m)}$ = –$\frac{(m-3)(m+3)•p}{(a+3)•4(m-3)}$ = –$\frac{p(m+3)}{4(a+3)}$.