Question

Divide.

http://i1255.photobucket.com/albums/hh639/zigzagoon20001/Equation.jpg

A. http://i1255.photobucket.com/albums/hh639/zigzagoon20001/A-2.jpg

B. http://i1255.photobucket.com/albums/hh639/zigzagoon20001/B-2.jpg

C. http://i1255.photobucket.com/albums/hh639/zigzagoon20001/C-2.jpg

D. http://i1255.photobucket.com/albums/hh639/zigzagoon20001/D-2.jpg

A, B, C, or D? Please explain (:

Answer 1

\[\frac{\frac{x^2 + 2x + 1}{x - 2}}{\frac{x^2 - 1}{x^2 - 4}}\]

note that both x^2 - 1 and x^2 - 4 are the difference of two squares, which means they can be written as (a + b)(a - b)

Also not that x^2 + 2x + 1 can be written as (x + 1)^2
So the problem becomes:
\[\frac{\frac{(x + 1)^2}{x - 2}}{\frac{(x - 1)(x + 1)}{(x - 2)(x + 2)}}\]

\[\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} \times \frac{d}{c}\]
Using that we get
\[\frac{(x + 1)^2(x - 2)(x + 2)}{(x - 2)(x - 1)(x + 1)}\]

cross out the factors that are the same:
\[\frac{(x + 1)(x + 2)}{(x - 1)}\]

It can't be simplified any futher, so the answer is A :)