how can i reduce and find the domain of the fraction "x³+x²-2/x-1" using factorization? :$

Question

Equality of algebaric fractions

Answer 1

1 | 1 1 0  -2

     1 1 2 | 2

     1 2 2 | 0 = x²+2x+2

x³+x²-2=(x-1)(x²+2x+2), therefore:

(x³+x²-2)/(x-1) simplifies to x²+2x+2 when x≠1, which is the domain. 

Limit as x→1 is 1+2+2=5 although the point (1,5) is undefined for the original expression.

For most intents and purposes, the expression x²+2x+2 is a valid substitute and the domain is unbounded. (The range is restricted to [1,∞).)