simplify the rational expression x^4+3x^3-2x^2-6x/x^3-2x stating all restrictions on the variable.

Answer 1

factor the top by grouping
x^3(x+3) - 2x(x+3)
= (x+3)(x^3 - 2x)

so wouldn't the last part cancel

so you end up with x+3

for the restriction, your divisor cannot be zero, i.e.
x^3-2x ≠ 0
x(x^2 - 2) ≠ 0
x ≠ 2 , ±√2