Question

упростите выражение 1/a+1 -a/a^2-1 : a/(a-1)^2 -3a+6/a+1

Answer 1

$displaystyle frac{1}{a+1}- frac{a}{a^2-1}: frac{a}{(a-1)^2} - frac{3a+6}{a+1}=\ \ \ = frac{1}{a+1}- frac{a}{(a-1)(a+1)} : frac{a}{(a-1)^2} - frac{3a+6}{a+1}=\ \ \ = frac{1}{a+1}- frac{a}{(a-1)(a+1)}cdot frac{(a-1)^2}{a} - frac{3a+6}{a+1}=\ \ \ = frac{1-a+1-3a-6}{a+1} = frac{-4a-4}{a+1}=- frac{4(a+1)}{a+1} =-4$