Question

How do you simplify `(w^2-16)/w * 3/(4-w)`?

Answer 1

`E = -(3(w+4))/w`

Explanation:

The first thing to notice here is that the numerator of the first fraction can be factored as the difference of two squares, for which you know that

`color(blue)(a^2 - b^2 = (a+b)(a-b))`

In your case, you will get

`w^2 - 16 = w^2 - 4^2 = (w+4)(w-4)`

Another important thing to notice is that you can factor the denominator of the second fraction by using `-1`

`4-w = -1 * [(-4) + w] = -(w-4)`

Your expression will thus be

`E = ( (w+4) color(red)(cancel(color(black)((w-4)))))/w * 3/(-color(red)(cancel(color(black)((w-4))))) = color(green)(-(3(w+4))/w)`