no i need them as binomals but i dont know what they would be, what would x^2 + x + 2 be factored out as to be in a (x ... )(x .... ) form as well as x^2 - 1
i dont know what those trinomals factor into to become binomals
@Mathnood768, you have no idea how any of this actually works.
If $\displaystyle x\ne\pm 1$ then multiply both sides by $\displaystyle x^2-1$.
We get:
$\displaystyle \\(x-1)(x^2+x+2)-x(x^2-1)=x^2-5\\x^3+x-2-x^3+x=x^2-5\\2x-2=x^2-5$