Question

Выполните пожалуйста всеее

Answer 1

1. 1)
$(frac{a}{3}-frac{a}{4}) * frac{2}{a^2} = frac{4a-3a}{12} * frac{2}{a^2} = frac{a}{12} * frac{2}{a^2} = frac{1}{6a^2}$

2)
$frac{a-1}{3a} : (1 - frac{1}{a}) = frac{a-1}{3a} : frac{a-1}{a} = frac{a-1}{3a} * frac{a}{a-1} = frac13$

3)
$(1+frac{y}{x}) : (1-frac{y}{x}) = frac{x+y}{x} : frac{x-y}{x} = frac{x+y}{x} * frac{x}{x-y} = frac{x+y}{x-y}$

2. 1)
$frac{a}{1-b}+frac{a-ab}{b^2-1} * frac{b+1}{a} = frac{a(1-b)}{(b-1)(b+1)} * frac{b+1}{a} - frac{a}{b-1} = -frac{a(b-1)}{(b-1)(b+1)} * frac{b+1}{a} - frac{a}{b-1} = \\ = -1-frac{a}{b-1} = frac{1-b-a}{b-1}$

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

3.
$1-frac{1}{1-frac{1}{x-3}} = 1 - frac{1}{frac{x-4}{x-3}} = 1-frac{x-3}{x-4} = frac{x-4-x+3}{x-4} = -frac{1}{x-4}$