how to simplify 2x^3-x-3/(x+1)

Answer 1

I'm assuming the 1st term was meant to be 2x^2; if not, the trinomial cannot be completely factored.

(2x^2 - x -3) (x + 1),
Factor the numerator:
A*C = 2 * -3 = -6 = 2 * -3,
2X^2 + (2X-3X) -3,
Group the 4 terms into factorable pairs:
(2x^2 + 2x) + (-3x - 3),
Factor each pair:
2x(x + 1) -3(x + 1),
Factor out x + 1 from each term:
(x + ) (2x - 3) = numerator,

(x + 1) (2x - 3) / (x + 1),
Cancel the x + 1 factors to get:
2x - 3.