How to simplify X squared - x - 12 divided by x squared - 9 over x squared - 3x?

Answer 1

To simplify the equation:
(x2 - x - 12) / [(x2 - 9) / (x2 - 3x)]

first, factor the numerator:
= (x + 3)(x - 4) / [(x2 - 9) / (x2 - 3x)]

Now bring the bottom term, (x2 - 3x), up to the top (remember, a/(b/c) = ac/b):

= (x + 3)(x - 4)(x2 - 3x) / (x2 - 9)

then factor the extra "x" out of the term (x2 - 3x):

= (x + 3)(x + 4)(x - 3)x / (x2 - 9)

now note that the bottom term is a difference of squares, and factor that out:

= (x + 3)(x + 4)(x - 3)x / (x + 3)(x - 3)

now you can see that the two terms on the bottom can be factored out of the top term, giving you:

x(x + 4)

which equals:

x2 + 4x