Ж: 1) 3/(x+y) + 2/x =; 2) a/(a+1) + 1/(a−1) =; 3) 4/(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) =.

Приводим дроби к общему знаменателю и упрощаем:

1. \(\frac3{x+y}+\frac2x=\frac{3x+2(x+y)}{x(x+y)}=\frac{5x+2y}{x(x+y)}\).
2. \(\frac a{a+1}+\frac1{a-1}=\frac{a(a-1)+(a+1)}{(a+1)(a-1)}=\frac{a^2+1}{a^2-1}\).
3. \(\frac4{x-3}-\frac1{x+3}=\frac{4(x+3)-(x-3)}{(x-3)(x+3)}=\frac{3x+15}{x^2-9}=\frac{3(x+5)}{x^2-9}\).
4. \(\frac{c-1}{c+2}-\frac{c-2}{c+1}=\frac{(c-1)(c+1)-(c-2)(c+2)}{(c+2)(c+1)}=\frac3{(c+2)(c+1)}\).
5. \(\frac{x+b}{3x}-\frac{x}{x+b}=\frac{(x+b)^2-3x^2}{3x(x+b)}=\frac{b^2+2bx-2x^2}{3x(x+b)}\).
6. \(\frac{a-b}{a+b}+\frac{a+b}{a-b}=\frac{(a-b)^2+(a+b)^2}{a^2-b^2}=\frac{2(a^2+b^2)}{a^2-b^2}\).
7. \(\frac{3ab-a^2}{(a-b)(a+b)}+\frac{2a}{a-b}=\frac{3ab-a^2+2a(a+b)}{(a-b)(a+b)}=\frac{a(a+5b)}{(a-b)(a+b)}\).
8. \(\frac{2y}{y-x}-\frac{3x}{y+x}=\frac{2y(y+x)-3x(y-x)}{(y-x)(y+x)}=\frac{2y^2-xy+3x^2}{y^2-x^2}\).