Упростите выражение (2/(1- x)^2+3/x^2-1)*(x-1)^2+1/x+1

Question

Упростите выражение
(2/(1- x)^2+3/x^2-1)*(x-1)^2+1/x+1

Answer 1

[2/(1-x)² + 3/(x²-1)]·(x-1)² + 1/(x+1) =
 {2/[(x-1)·(x-1)] + 3/[(x+1)·(x-1)]} ·(x-1)² +1/(x+1) =      
                     общ. зн. (x-1)²·(x+1)
  = {[2·(x+1) + 3·(x-1)]·(x-1)²} /[(x-1)²·((x+1)] + (x-1)²/[(x-1)²·(x+1)] =
  = [(2x+2 +3x -3)·(x-1)² + (x-1)²]/[(x-1)²·(x+1)] =
       = [(5x -1 +1) ·(x-1)²]/[(x-1)².(x+1)] =
       = 5x/(x+1)