Question

(X^2-4)/(x-1) divide the polynomial

Answer 1

`=x+2`

Explanation:

`(x^(2)-4 )/(x-2) \\=((x+2)(x-2))/((x-2)) \\=x+2`

Answer 2

Answer:
`x+1-(3)/(x-1)`

Explanation:

You can use long division or synthetic division. Whichever method you choose, remember to include a zero for the missing term (0x)

Synthetic division: x - 1 = 0 --> x = 1

`1 |\ \ 1\quad 0\quad -4\\.\ |\underline{\ \downarrow \quad 1\qquad 1}\\.\quad 1\quad 1\quad \boxed{-3}\quad \leftarrow \text{Remainder}\\\\\\=x + 1 + (-3)/(x-1)`

Long Division:

`.\qquad \underline{\ \ x+1\qquad \ }\\x-1)x^2+0x-4\\.\qquad \underline{-x^2+1x}\ \ \downarrow\\.\qquad \qquad \quad 1x-4\\.\qquad \qquad \quad \underline{-x+1}\\.\qquad \qquad \qquad \ \ \boxed{-3}\quad \leftarrow \text{Remainder}\\\\\\=x + 1 + (-3)/(x-1)`