Question

Выражения 1)a+2/a-2 * (2a^2-a-3/a^2+5a+6 : 2a-3/a-2) 2)(2+1/b) : 8b^2+8b+2/b^2-4b * 2b+1/b

Answer 1

$\frac{a+2}{a-2} * (\frac{2a^2-a-3}{a^2+5a+6} : \frac{2a-3}{a-2}) \\ \\ 1) \frac{2a^2-a-3}{a^2+5a+6} : \frac{2a-3}{a-2}=\frac{(a+1)(2a-3)}{(a+2)(a+3)} : \frac{2a-3}{a-2}=\frac{(a+1)(2a-3)}{(a+2)(a+3)} *\frac{a-2}{2a-3}= \\ \\ =\frac{(a+1)(a-2)}{(a+2)(a+3)} \\ \\ 2) \frac{a+2}{a-2} *\frac{(a+1)(a-2)}{(a+2)(a+3)}=\frac{a+1}{a+3}$

$(2+ \frac{1}{b}) : \frac{8b^2+8b+2}{b^2-4b} * \frac{2b+1}{b} \\ \\ 1) 2+ \frac{1}{b}= \frac{2b+1}{b} \\ \\ 2)\frac{2b+1}{b}: \frac{8b^2+8b+2}{b^2-4b} =\frac{2b+1}{b}: \frac{2(2b+1)^2}{b(b-4)}= \frac{2b+1}{b}* \frac{b(b-4)}{2(2b+1)^2}=\frac{b-4}{2(2b+1)} \\ \\ 3) \frac{b-4}{2(2b+1)}* \frac{2b+1}{b}=\frac{b-4}{2b}$