Раздел «Ж», правый столбец: 2) a/(a−1) + 1/(a−1) =; 3) 1/(x−3) − 1/(x+3) =; 4) (c−1)/(c+2) − (c−2)/(c+1) =; 5) (x+b)/(3x) − x/(x+b) =; 6) (a−b)/(a+b) + (a+b)/(a−b) =; 7) (3ab−a²)/[(a−b)(a+b)] + 2a/(a−b) =; 8) 2y/(y−x) − 3x/(y+x) =.

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Accepted Answer

Приводим дроби к общему знаменателю и упрощаем:

\(\frac{a}{a-1}+\frac{1}{a-1}=\frac{a+1}{a-1}\).
\(\frac{1}{x-3}-\frac{1}{x+3}=\frac{(x+3)-(x-3)}{(x-3)(x+3)}=\frac{6}{x^2-9}\).
\(\frac{c-1}{c+2}-\frac{c-2}{c+1}=\frac{3}{(c+2)(c+1)}\).
\(\frac{x+b}{3x}-\frac{x}{x+b}=\frac{(x+b)^2-3x^2}{3x(x+b)}\).
\(\frac{a-b}{a+b}+\frac{a+b}{a-b}=\frac{2(a^2+b^2)}{a^2-b^2}\).
\(\frac{3ab-a^2}{(a-b)(a+b)}+\frac{2a}{a-b}=\frac{a(a+5b)}{a^2-b^2}\).
\(\frac{2y}{y-x}-\frac{3x}{y+x}=\frac{2y^2-xy+3x^2}{y^2-x^2}\).

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