How do I solve this rational division question? I'm solving this rational expression question and I'm stuck. What should I do next?
My work is below. 
Thank you!



If you don't know yet, verify yourself that $(x-a)(x-b)=x^2-(a+b)x+ab$ which means that the roots $a,b$ of $x^2-Ux+V$ will just satisfy $U=a+b$ and $V=ab$.
Knowing this, you can easily find integer roots by simple tries for a quadratic with small coefficients, e.g. for $x^2+x-2$ we look for $a,b$ such that $a+b=-1$ and $ab=-2$, so it is $-2$ and $1$, hence $x^2+x-2=(x+2)(x-1)$.
You can do it, but you need to pay more attention. E.g. the fractions (after taking the reciprocal of the divisor) has to be multiplied, but in your solution, the nominators were added.
And, at step #2 VI), you seem to cancel $x^3$, please forget it, because it is a summand of both the nominator and the denumerator, and not a multiplier.
