Question

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

Answer 1

Answer:

$=x+2$

Step-by-step explanation:

$\frac{x^{2}-4 }{x-2} \\=\frac{(x+2)(x-2)}{(x-2)} \\=x+2$

Answer 2

Answer:   $x+1-\dfrac{3}{x-1}$

Step-by-step 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

$1 |\ \ 1\quad 0\quad -4\\.\ |\underline{\ \downarrow \quad 1\qquad 1}\\.\quad 1\quad 1\quad \boxed{-3}\quad \leftarrow \text{Remainder}\\\\\\=x + 1 + \dfrac{-3}{x-1}$

Long Division:

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