How do I divide (x^3)-2 by (x^2)-1 ?

Question

This was my attempt. I got stuck..

x + 1
____________________
x^3 + x^2 + x - 2
-x^3 - x
____________________
x^2 + 2x - 2
-x^2 + 1
______________
2x - 1


The correct answer should be x + ( (x-2)/(x^2 - 1) )

This was my attempt. I got stuck..

x + 1
____________________
x^3 + x^2 + x - 2
-x^3 - x
____________________
..........x^2 + 2x - 2
..........-x^2 + 1
______________
....................2x - 1

Answer 1

x^2-1)x^3-2(x
...........x^3-x
_______________
................x - 2

quotient is x and remainder is x-2

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

Answer 2

If you use long division

x^3+0*x^2+0*x-2 /( x^2-1)
-x^3 +x ( x )quotient
_______________
( x -2 )remainder so
x^3-2= x+ (x-2)/x^2-1)