Question

I am trying to write this rational expression in its simplest form:

2-x+2x^2-x^3/x^2-4

However I have no idea how to factor the four numbers on the top. I"m used to factoring just three numbers. Can you show me how to do this? Thanks!!!

Answer 1

use grouping
2-x+2x^2-x^3
= (2-x) + x^2(2-x)
= (2-x)(1+x^2)

so
(2-x+2x^2-x^3)/(x^2-4)
= (2-x)(1+x^2)/[(x-2)(x+2)]
= -(1+x^2)/(x+2)

Answer 2

2x+4x-3x/2x-4=
6x-3x/2x-4= 5/10x