Simplifying Complex Fractions - Part 1

In looking at complex fractions, you'll notice that you will have a fraction in the numerator and a fraction in the denominator to be a fraction as a whole. What we must understand is this line here means division. So we just simply go about it by rewriting it if we want to where it simply turns out to be a division problem. So we have equals and we apply the whole idea of keeping the first fraction, put our division and keeping the last fraction. Then once we do this division, we actually use that idea of keep, change, flip. So, we keep the first, change the division sign to multiplication, and then flip the last. So from here, notice since there is an x plus 2 up in the numerator and an x plus 2 in the denominator, we can go ahead and cancel those out, leaving us with 5 divided by x. Now, method two! Here is a different method that many teachers use. If you notice that you have the same denominator in both fractions, then you can go ahead and multiply each fraction by that denominator. So let’s say I have x plus 2 here, and multiplying by an x plus 2, because essentially all you are really doing really is multiplying by 1. So, you're not changing the quantity of anything you are changing the way it looks. Manipulating a little bit. So from here I can say that my x plus 2's cancel out on both of them, and then I just get 5 divided by x. It is the same thing that we got in the previous method.