Question

помогите!!! алгебра. преобразование алгебраических выражений!!

Answer 1

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