13:57 1164_2_algebra_7kl_... 81% a) (a/b - b/a) * 3ab/(a+b), б) (3a+7b/5a + 8a-3b/5b) * 10ab/(7b^2+8a^2). 2. Выполните действия: a) (a-y/a-b - b-y/a+b) : 1/(a^2-b^2), б) (x/(2-4x) - 5x/(4x+2)) : (9x^2-3x)/(1-4x+4x^2). 3. Решите уравнение: ((2x - 1)^2)/6 + ((x - 1)(x - 2))/3 = x^2.

1. Упростите выражения:

a)

\[\left(\frac{a}{b} - \frac{b}{a}\right) \cdot \frac{3 a b}{a+b} = \frac{a^2 - b^2}{a b} \cdot \frac{3 a b}{a+b} = \frac{(a-b)(a+b)}{a b} \cdot \frac{3 a b}{a+b} = 3(a-b)\]

б)

\[\left(\frac{3 a+7 b}{5 a}+\frac{8 a-3 b}{5 b}\right) \cdot \frac{10 a b}{7 b^{2}+8 a^{2}} = \frac{3 a b+7 b^{2}+8 a^{2}-3 a b}{5 a b} \cdot \frac{10 a b}{7 b^{2}+8 a^{2}} = \frac{8 a^{2}+7 b^{2}}{5 a b} \cdot \frac{10 a b}{7 b^{2}+8 a^{2}} = 2\]

2. Выполните действия:

a)

\[\left(\frac{a-y}{a-b} - \frac{b-y}{a+b}\right) : \frac{1}{a^{2}-b^{2}} = \frac{(a-y)(a+b) - (b-y)(a-b)}{(a-b)(a+b)} : \frac{1}{a^{2}-b^{2}} = \frac{a^{2}+a b-a y-b y - (a b-b^{2}-a y+b y)}{(a-b)(a+b)} : \frac{1}{a^{2}-b^{2}} = \frac{a^{2}+a b-a y-b y - a b+b^{2}+a y-b y}{(a-b)(a+b)} : \frac{1}{a^{2}-b^{2}} = \frac{a^{2}-2 b y+b^{2}}{(a-b)(a+b)} : \frac{1}{a^{2}-b^{2}} = \frac{(a-b)^{2}+2 a b-2 b y}{(a-b)(a+b)} \cdot (a-b)(a+b) = (a-b)^{2}+2 a b-2 b y = a^{2}-2 a b+b^{2}+2 a b-2 b y = a^{2}+b^{2}-2 b y\]

б)

\[\left(\frac{x}{2-4 x} - \frac{5 x}{4 x+2}\right) : \frac{9 x^{2}-3 x}{1-4 x+4 x^{2}} = \left(-\frac{x}{4 x-2} - \frac{5 x}{4 x+2}\right) : \frac{3 x(3 x-1)}{(2 x-1)^{2}} = \frac{-x(4 x+2)-5 x(4 x-2)}{(4 x-2)(4 x+2)} : \frac{3 x(3 x-1)}{(2 x-1)^{2}} = \frac{-4 x^{2}-2 x-20 x^{2}+10 x}{16 x^{2}-4} : \frac{3 x(3 x-1)}{(2 x-1)^{2}} = \frac{-24 x^{2}+8 x}{4(4 x^{2}-1)} : \frac{3 x(3 x-1)}{(2 x-1)^{2}} = \frac{8 x(-3 x+1)}{4(2 x-1)(2 x+1)} \cdot \frac{(2 x-1)^{2}}{3 x(3 x-1)} = \frac{2 (-3 x+1)}{(2 x+1)} \cdot \frac{(2 x-1)}{3 (3 x-1)} = -\frac{2(3x-1)(2x-1)}{3(2x+1)(3x-1)} = -\frac{2(2x-1)}{3(2x+1)}\]

3. Решите уравнение:

\[\frac{(2 x-1)^{2}}{6}+\frac{(x-1)(x-2)}{3} = x^{2}\] \[\frac{4 x^{2}-4 x+1}{6}+\frac{x^{2}-3 x+2}{3} = x^{2}\] \[\frac{4 x^{2}-4 x+1}{6}+\frac{2 x^{2}-6 x+4}{6} = x^{2}\] \[\frac{4 x^{2}-4 x+1+2 x^{2}-6 x+4}{6} = x^{2}\] \[\frac{6 x^{2}-10 x+5}{6} = x^{2}\] \[6 x^{2}-10 x+5 = 6 x^{2}\] \[-10 x = -5\] \[x = \frac{1}{2}\]