[SOUND] Let's look at Simplifying Fractions.

For example, let's simplify this expression here.

Now, these types of fractions where the numerator or the denominator or both

contain a fraction are often referred to as either Complex Fractions or Compound

Fractions. However, don't confuse the word complex

here with the complex number. System.

Now remember, when we're dividing 2 fractions, we multiply the numerator by

the reciprocal of the denominator. That is, we flip the bottom fraction, and

multiply. And when we multiply fractions, we

multiply the numerators. And we multiply the denominators.

And now this x^2 - 9 will factor. It's a difference of two squares, which

gives us 5 * 3 + x / 15x * and this factors into x + 3 * x - 3.

Now, x + 3 and 3 + x will cancel, and we're assuming here of course that x is

not equal negative 3. And 5 goes into 15, 3 times, so we'll

have a 3 left here in the denominator. And therefore, our answer is 1 / 3x

(x-3). Alright, let's see another example.

Let's simplify this fraction. Now, there are different approaches here.

For example, we could work with the numerator separately and then work with

the denominator separately. However the method that students seem to

like best when working with this type of fraction, is to first eliminate.

These denominators here and we can do that by multiplying both the numerator

and denominator by the least common multiple of the denominators, which in

this case is their product x times y. So lets do that.

We'll multiply the numerator by x times y, as well as the denominator.

Again when multiplying fractions, we multiply the numerators.