• 1. Выполните действия: a) 5a+5b. b б) xy-x : 62 y2-1 a+b'; B) (-2a3)2; r) (a2-x²): 2+2x a

а) \[\frac{5a+5b}{b^2} \cdot \frac{b}{a+b} = \frac{5(a+b)}{b^2} \cdot \frac{b}{a+b} = \frac{5(a+b)b}{b^2(a+b)} = \frac{5}{b}\]

б) \[\frac{y}{xy-x} : \frac{y}{y^2-1} = \frac{y}{x(y-1)} : \frac{y}{(y-1)(y+1)} = \frac{y}{x(y-1)} \cdot \frac{(y-1)(y+1)}{y} = \frac{y(y-1)(y+1)}{x(y-1)y} = \frac{y+1}{x}\]

в) \[\left(-\frac{2a^3}{b^4}\right)^2 = \frac{(-2a^3)^2}{(b^4)^2} = \frac{4a^6}{b^8}\]

г) \[(a^2-x^2) : \frac{2a+2x}{a} = (a-x)(a+x) : \frac{2(a+x)}{a} = (a-x)(a+x) \cdot \frac{a}{2(a+x)} = \frac{(a-x)(a+x)a}{2(a+x)} = \frac{(a-x)a}{2}\]

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