Correct option is (c) 0
\(\frac{x + 2}{(x+1)(2x + 3)} - \frac{2x + 3}{(x + 1)(x + 2)} + \frac{3x + 5}{(2x + 3) (x + 2)}\)
\(= \frac{(x + 2)^2 - (2x + 3)^2 + (x + 1) (3x + 5)}{(x + 1)(x + 2)(2x + 3)}\)
\(= \frac{(x^2 + 4x + 4) - (4x^2 + 12x + 9)+ (3x^2 + 8x + 5)}{(x + 1) (x + 2) (2x + 3)}\)
\(= \frac{(4x^2 + 12x + 9)- (4x^2 + 12x + 9)}{(x + 1)(x + 2) (x + 3)}\)
\(= \frac{0}{(x + 1)(x + 2) (x + 3)}\)
\(= 0\)
