Perform operations and simplify x3x2 x 2 4x2 x 6 xx2

Perform operations and simplify x^3/x^2 - x - 2 - 4/x^2 + x - 6 + x/x^2 + 4x + 3

Use factorisation of denominator polynomial

x^2-x-2 = (x-2)(x+1)

x^2+x-6 = (x+3)(x-2)

x^2+4x+3 = (x+3)(x+1)

Take LCM of last two teen first

x^2-6x-4/(x-3)(x+1)(x-2)

Now take LCM of this with first term

x^4-3x^3+x^2-6x-4/(x-3)(x-2)(x+1)