2. Преобразуйте в дробь выражения. Вариант Б1: а) \(\frac{x+2}{x+3}-\frac{x-1}{x}\); б) \(2y-\frac{4y^2}{2y-1}-1\); в) \(\frac{5a^2}{5ab-b^2}-\frac{b}{25a-5b}\); г) \(\frac{x^2}{x^3-x}+\frac{1}{2-2x}\). Вариант Б2: а) \(\frac{x}{x-4}-\frac{x+2}{x-2}\); б) \(6y+\frac{12y}{6y-1}-1\); в) \(\frac{a}{3a-9b}-\frac{3b^2}{a^2-3ab}\); г) \(\frac{x^2}{x^3-4x}+\frac{1}{4-2x}\).

Вариант Б1

1. \(\frac{x+2}{x+3}-\frac{x-1}{x}=\frac{x(x+2)-(x-1)(x+3)}{x(x+3)}=\frac{3}{x(x+3)}\).
2. \(2y-\frac{4y^2}{2y-1}-1=\frac{(2y-1)^2-4y^2}{2y-1}=\frac{1-4y}{2y-1}\).
3. \(\frac{5a^2}{5ab-b^2}-\frac{b}{25a-5b}=\frac{25a^2-b^2}{5b(5a-b)}=\frac{(5a-b)(5a+b)}{5b(5a-b)}=\frac{5a+b}{5b}\).
4. \(\frac{x^2}{x^3-x}+\frac{1}{2-2x}=\frac{x}{x-1}-\frac{1}{2(x-1)}=\frac{2x-1}{2(x-1)}\).

Вариант Б2

1. \(\frac{x}{x-4}-\frac{x+2}{x-2}=\frac{x(x-2)-(x+2)(x-4)}{(x-4)(x-2)}=\frac{8}{(x-4)(x-2)}\).
2. \(6y+\frac{12y}{6y-1}-1=\frac{(6y-1)^2+12y}{6y-1}=\frac{36y^2+1}{6y-1}\).
3. \(\frac{a}{3a-9b}-\frac{3b^2}{a^2-3ab}=\frac{a^2-9b^2}{3a(a-3b)}=\frac{a+3b}{3a}\).
4. \(\frac{x^2}{x^3-4x}+\frac{1}{4-2x}=\frac{x}{(x-2)(x+2)}-\frac{1}{2(x-2)}=\frac{1}{2(x+2)}\).