[SOUND]. Let's see some examples of dividing

rational expressions. [SOUND].

For example, let's divide 2x ^ 4 y ^ 2 / 5y by 4x / 15y.

Now dividing by this is the same as multiplying by its reciprocal.

In other words this is equal (2x^4y^2) / 5y.

And then times, remember with the reciprocal we flip.

So this is 15y / 4x. And when we multiply fractions, we

multiply the numerators, and then multiply the denominators.

So this would be equal to 2 times 15, which is 30.

And then x ^ 4 times y squared times y, which is y cubed.

Divided by 5 times 4 is 20, and then we have x times y.

Now 20 and 30 are both divisible by 10, so we'd be left with a 2 here and a 3

here. And then we can cancel this x with one of

the x's in the numerator, which would leave us with x cubed

leftover in the numerator, and we're assuming here of course that X

does not equal 0. And then we're cancelling one of the y's,

which leaves us with Y squared in the numerator.

Again we're assuming Y does not equal 0, which would leave us with our answer of

3x cubed, y squared divided by 2.

Let's look at another example. [SOUND] Let's divide these two rational

expressions. Again, we'll begin by multiplying by the

reciprocal of this. Namely, this equal to (4X - 4) / (2X + 3)

times, and then we flip the second rational expression, so you have (2X ^ 2

+ 5X + 3) / (2X ^ 2 - X - 1). Again we multiply the numerators and

multiply the denominators. So this is 4x - 4 * 2x ^ 2 + 5x + 3 / 2x

+ 3 * 2x squared minus x minus 1. And now we'll factor. We'll begin by

pulling a 4 out of this first term. So we have 4 times x-1 and then this

factors into 2x plus 3 times x plus 1, all divided by 2x plus 3. Then this

factors into 2x plus 1 times x minus 1. And now, the (x-1)'s will cancel, and

we're assuming here of'course that x does not equal , as well as is (2x+3)'s, and

we are assuming here that x does not equal negative 3 halfs, which leaves us

with our answer 4 (x+1). Divided by 2 X plus 1.

And this is how we divide rational expressions.

Thank you and we'll see you next time. [SOUND]