Question

Упростите выражение:
$frac{5x+6}{ x^2-4 } - frac{x}{x^2-4} : frac{x}{x-2} - frac{x+2}{x-2}$

Answer 1

(5x + 6) / ( x^2 - 4) - x/ (x-2) (x+2) * (x - 2) /x - (x+2) / (x-2) =
(5x + 6) / ( x^2 - 4) - 1/ (x+2) - (x +2) / (x-2) = 
(5x  + 6 - (x - 2) - (x+2) (x+2)) / ((x-2)(x+2)) = 
(5x + 6 -x + 2 - x^2 - 2x - 2x - 4) / ((x-2)(x+2)) = 
- x^2 - 4 / ((x-2)(x+2)) = 
- (x-2)(x+2) / ((x-2)(x+2)) = - 1