В-2. 2. Выполните действия: 1) $\frac{x+4}{2x-6}-\frac{x+1}{x-3}$; 2) $\frac{a+3}{3a-3}+\frac{2-a}{5a-5}$; 3) $\frac{x+5}{x-5}-\frac{x-1}{x+5}$; 4) $\frac{4b}{3b-21}+\frac{3b}{14-2b}$; 5) $\frac{3p}{3p+2q}-\frac{9p^2}{9p^2+12pq+4q^2}$; 6) $\frac{4}{c^2-36}-\frac{2}{c^2-6c}$.

Question

Вопрос: $Фото задания: В-2. 2. Выполните действия: 1) $\frac{x+4}{2x-6}-\frac{x+1}{x-3}$; 2) $\frac{a+3}{3a-3}+\frac{2-a}{5a-5}$; 3)…$ Фото задания

Accepted Answer

\[\frac{x+4}{2(x-3)}-\frac{x+1}{x-3}=\frac{x+4-2(x+1)}{2(x-3)}=\frac{2-x}{2(x-3)}.\]
\[\frac{a+3}{3(a-1)}+\frac{2-a}{5(a-1)}=\frac{5(a+3)+3(2-a)}{15(a-1)}=\frac{2a+21}{15(a-1)}.\]
\[\frac{(x+5)^2-(x-1)(x-5)}{(x-5)(x+5)}=\frac{16x+20}{x^2-25}=\frac{4(4x+5)}{x^2-25}.\]
Так как $14-2b=-2(b-7)$, то
\[\frac{4b}{3(b-7)}-\frac{3b}{2(b-7)}=\frac{8b-9b}{6(b-7)}=-\frac{b}{6(b-7)}.\]
\[\frac{3p}{3p+2q}-\frac{9p^2}{(3p+2q)^2}=\frac{3p(3p+2q)-9p^2}{(3p+2q)^2}=\frac{6pq}{(3p+2q)^2}.\]
\[\frac{4}{(c-6)(c+6)}-\frac{2}{c(c-6)}=\frac{4c-2(c+6)}{c(c-6)(c+6)}=\frac{2(c-6)}{c(c-6)(c+6)}=\frac{2}{c(c+6)}.\]

Ответ: $\frac{2-x}{2(x-3)};\ \frac{2a+21}{15(a-1)};\ \frac{4(4x+5)}{x^2-25};\ -\frac{b}{6(b-7)};\ \frac{6pq}{(3p+2q)^2};\ \frac{2}{c(c+6)}$.