1. Упростите выражение:

1) а) $\frac{2b^2-3b+4}{(b-1)^2} - \frac{b-2}{b-1} = \frac{2b^2-3b+4 - (b-2)(b-1)}{(b-1)^2} = \frac{2b^2-3b+4 - (b^2-3b+2)}{(b-1)^2} = \frac{b^2+2}{(b-1)^2}$ б) $\frac{1-2c}{c^3-1} - \frac{c-1}{c^2+c+1} = \frac{1-2c - (c-1)(c-1)}{(c-1)(c^2+c+1)} = \frac{1-2c - (c^2-2c+1)}{(c^3-1)} = \frac{-c^2}{c^3-1}$ 2) а) $\frac{2x-1}{6-3x} + \frac{2x+1}{2x-4} - \frac{x+3}{6x-12} = \frac{2x-1}{-3(x-2)} + \frac{2x+1}{2(x-2)} - \frac{x+3}{6(x-2)} = \frac{-2(2x-1) + 3(2x+1) - (x+3)}{6(x-2)} = \frac{-4x+2+6x+3-x-3}{6(x-2)} = \frac{x+2}{6(x-2)}$ б) $\frac{2a}{a-5} - \frac{5}{a+5} + \frac{2a^2}{25-a^2} = \frac{2a}{a-5} - \frac{5}{a+5} - \frac{2a^2}{a^2-25} = \frac{2a(a+5) - 5(a-5) - 2a^2}{(a-5)(a+5)} = \frac{2a^2+10a-5a+25-2a^2}{(a-5)(a+5)} = \frac{5a+25}{(a-5)(a+5)} = \frac{5(a+5)}{(a-5)(a+5)} = \frac{5}{a-5}$ 3) а) $\frac{3}{2y+6} + \frac{y^2-y-3}{y^2-9} - 1 = \frac{3}{2(y+3)} + \frac{y^2-y-3}{(y-3)(y+3)} - 1 = \frac{3(y-3) + 2(y^2-y-3) - 2(y^2-9)}{2(y-3)(y+3)} = \frac{3y-9+2y^2-2y-6-2y^2+18}{2(y^2-9)} = \frac{y+3}{2(y-3)(y+3)} = \frac{1}{2(y-3)}$ б) $1 - \frac{2b+1}{b^3+1} - \frac{b}{b+1} = \frac{(b^2-b+1) - (2b+1) - b(b^2-b+1)}{b^3+1} = \frac{b^2-b+1-2b-1-b^3+b^2-b}{b^3+1} = \frac{-b^3+2b^2-4b}{b^3+1}$ 2) а) $\frac{a^2-x^2}{b^2-16} \cdot \frac{b+4}{a-x} + \frac{x}{4-b} = \frac{(a-x)(a+x)(b+4)}{(b-4)(b+4)(a-x)} - \frac{x}{b-4} = \frac{a+x}{b-4} - \frac{x}{b-4} = \frac{a}{b-4}$ б) $\frac{x-y}{2x+y} + \frac{1}{x-y} \cdot \frac{x^2-y^2}{2x+y} = \frac{x-y}{2x+y} + \frac{(x-y)(x+y)}{(x-y)(2x+y)} = \frac{x-y+x+y}{2x+y} = \frac{2x}{2x+y}$ в) $(\frac{2a^2-a}{a^2-a+1} - 2) : (\frac{1}{a+1} - \frac{a-1}{a^2-a+1}) = \frac{2a^2-a-2a^2+2a-2}{a^2-a+1} : \frac{a^2-a+1-(a-1)(a+1)}{(a+1)(a^2-a+1)} = \frac{a-2}{a^2-a+1} : \frac{a^2-a+1-(a^2-1)}{(a+1)(a^2-a+1)} = \frac{a-2}{a^2-a+1} \cdot \frac{(a+1)(a^2-a+1)}{2-a} = \frac{a-2}{1} \cdot \frac{-(a+1)}{a-2} = -(a+1) = -a-1$