(x^4+2x^3-7)÷(x^2-1) =
x^2 + 2x + 1
--------------------------------------
x^2 -1 [ x^4 + 2x^3 + 0x^2 + 0x - 7 ]
x^4 - x^2
------------------------------------------------
2x^3 + x^2
2x^3 -2x
---------------------------------------------------
x^2 + 2x - 7
x^2 - 1
----------------
2x - 6
So, our answer is x^2 + 2x + 1 + [2x -6] / [x^2 -1]
(x^4+2x^3-7)÷(x^2-1) =
x^2 + 2x + 1
--------------------------------------
x^2 -1 [ x^4 + 2x^3 + 0x^2 + 0x - 7 ]
x^4 - x^2
------------------------------------------------
2x^3 + x^2
2x^3 -2x
---------------------------------------------------
x^2 + 2x - 7
x^2 - 1
----------------
2x - 6
So, our answer is x^2 + 2x + 1 + [2x -6] / [x^2 -1]