How do we simplify complex fractions?

How do we simplify complex fractions?

Complex fractions are really solved the same way rational expressions. 

When you add or subtract you have to have a common denominator, when you divide you use the KCF method, and when you multiply you just need to remember to simplify. 

But with complex fractions you'll get fractions like these:

With a problem like this you'd just re-write the problem so that it looks normal, and then do the same as division. Use the KCF method. 

But just remember that before you "flip over", re-write the fraction out. Incase of any mistakes or anything. 

That's it for that part, but if you get a real complex fractions with things you don't know ... Here's and example:

You're just like -_- " what is this? "

Well let's break it down. Let's being with simplifying the numerator.

You'll get:

because you have to have a
common denominator
when adding fractions.

Which simplifies to:

Now for the denominator it's look like:

common denominator !

And simplify to:

So now that we've simplified the numerator and denominator, you'll plug it back in and re-write the problem. 

⬇

KCF method

Cross out common factors

Then your answer would simply be:

Because it wouldn't be simplified more than that.

So that's basically it !

Sources:

1. John Schnatterly: johnschnatterly.blogspot.com
2. http://www.purplemath.com/modules/compfrac.htm
3. http://www.basic-mathematics.com/examples-of-complex-fractions.html