Question

Помогите пожалуйста. Даю 100 баллов. Алгебра, 8 класс

Answer 1

4)
$frac{2a^2-2}{a-3}(frac{2}{a+1}-frac{1}{a-1}) + 3a = frac{2(a-1)(a+1)}{a-3}*frac{2(a-1)-a-1}{(a-1)(a+1)} + 3a = \\ =frac{2(a-1)(a+1)}{a-3}*frac{2a-2-a-1}{(a-1)(a+1)}+3a = frac{2(a-1)(a+1)}{a-3}*frac{a-3}{(a-1)(a+1)}+3a = 3a+2\\ frac{1}{3} textless a textless frac{1}{2}\\ 1 textless 3a textless 1.5\\ 3 textless 3a+2 textless 3.5$
Ответ: $(3;3.5)$

5)
$frac{1}{t} = frac{1}{a} + frac{1}{b}\\ frac{1}{t} = frac{a + b}{ab}\\ t = frac{ab}{a+b}$
$5 leq a leq 8\ 20 leq b leq 24\ 100 leq ab leq 192\ 25 leq a+b leq 32$
$frac{1}{32} leq frac{1}{a+b} leq frac{1}{25}\\ frac{100}{32} leq frac{ab}{a+b} leq frac{192}{25}\\ 3frac{1}{8} leq frac{ab}{a+b} leq 7frac{17}{25}\\ t in [4;7]$