Answer:
[tex]=x+2[/tex]
Step-by-step explanation:
[tex]\frac{x^{2}-4 }{x-2} \\=\frac{(x+2)(x-2)}{(x-2)} \\=x+2[/tex]
Answer: [tex]x+1-\dfrac{3}{x-1}[/tex]
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
[tex]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}[/tex]
Long Division:
[tex].\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}[/tex]
