we have that
[(x²+2x+1)/(x-2)]/[(x²-1)/(x²-4)]
we know that
(x²+2x+1)---------> (x+1)²
(x²-1)------> (x+1)*(x-1)
(x²-4)----->(x+2)*(x-2)
so
[(x+1)²/(x-2)]/[(x+1)*(x-1)/(x+2)*(x-2)]
[(x+1)²*(x+2)*(x-2)]/[(x-2)*(x+1)/(x-1)]
[(x+1)*(x+2)]/[(x-2)*(x-1)]
the answer is
[(x+1)*(x+2)]/[(x-2)*(x-1)]