We're trying to evaluate a fractional expression here:
[tex]\frac{2x + 2}{x -4} * \frac{3x - 12}{x^{2} + 6x + 5}[/tex]
The first thing to do, is factor everything we can. The quadratic factors to (x + 1)(x+5) and the expression above that factors to 3(x - 4). 2x + 2 factors to 2(x + 1).
[tex]\frac{2(x + 1)}{x -4} * \frac{3(x - 4)}{(x+1)(x+5)}[/tex]
It looks a little complicated now, but if we combine the two we can cancel some stuff.
[tex]\frac{2(x + 1) * 3(x - 4)}{(x -4)(x+1)(x+5)}[/tex]
Still looking complicated, but look, we have (x+1) and (x+4) on the top and the bottom, that means they don't matter and we can get rid of them:
[tex]\frac{2 * 3}{x+5} = \frac{6}{x+5}[/tex]
Tada! The area is 6/(x+5). We'd need to know x to go any further!
Need any more explanation?
