А1. Выполните действия: a) 3a-9 3b+6 : b+2 18a-54 б) (a-2)² 3a-6 : b+5 2b+10 в) 2x : 5x-10 x x-2

a) $$\frac{3a-9}{b+2} : \frac{3b+6}{18a-54}$$ = $$\frac{3(a-3)}{b+2} : \frac{3(b+2)}{18(a-3)}$$ = $$\frac{3(a-3)}{b+2} \cdot \frac{18(a-3)}{3(b+2)}$$ = $$\frac{3 \cdot 18 (a-3)(a-3)}{3(b+2)(b+2)}$$ = $$\frac{18(a-3)^{2}}{(b+2)^{2}}$$.

Ответ: $$\frac{18(a-3)^{2}}{(b+2)^{2}}$$.

б) $$\frac{(a-2)^{2}}{b+5} : \frac{3a-6}{2b+10}$$ = $$\frac{(a-2)^{2}}{b+5} : \frac{3(a-2)}{2(b+5)}$$ = $$\frac{(a-2)^{2}}{b+5} \cdot \frac{2(b+5)}{3(a-2)}$$ = $$\frac{2(a-2)(a-2)(b+5)}{3(b+5)(a-2)}$$ = $$\frac{2(a-2)}{3}$$.

Ответ: $$\frac{2(a-2)}{3}$$.

в) $$\frac{2x}{5x-10} : \frac{x}{x-2}$$ = $$\frac{2x}{5(x-2)} : \frac{x}{x-2}$$ = $$\frac{2x}{5(x-2)} \cdot \frac{x-2}{x}$$ = $$\frac{2x(x-2)}{5x(x-2)}$$ = $$\frac{2}{5}$$.

Ответ: $$\frac{2}{5}$$.