[(x^2+4x+3)/(2x^2-x-10)]*[(2x^2+4x^3)/(x^2+3x)]*[(x)/(x^2+3x+2)]
x^2+4x+3 = (x+1)(x+3
2x^2-x-10 = (2x-5)(x+2)
2x^2+4x^3 = 2x^2(2x+1)
x^2+3x = x(x+3)
x^2+3x+2 = (x+1)(x+2)
so, you have
(x+1)(x+3)(2x^2)(2x+1)(x)
-----------------------------
(2x-5)(x+2)(x)(x+3)(x+1)(x+2)
2x^2(2x+1)
--------------------
(2x-5)(x+2)^2