As if REs are not complex enough, now we add REs inside other REs (AKA Fractions Within Fractions). An example: $$\frac{\frac{4}{y}}{6-\frac{3}{y}}$$ These look menacing, but turn out to be quite simple. The key is to be able to build common denominators (from previous topic on Add/Sub REs). The follwing videos show two different methods used to simplify these complex fractions. Again, it does not matter which method you choose, but select the one that makes the most sense to you.
The idea here is to get a CD of the numerator and simplify just the numerator into one single RE. Then get a CD of the denominator and simplify just the denominator into one single RE. Now the problem is a division problem from the first topic in the RE section, multiply by the reciprocal of the denominator.
Example Simplify the following complex fraction (Method 1):
$$\frac{\frac{1}{a}-\frac{1}{b}}{\frac{1}{a^2}-\frac{1}{b^2}}$$The idea here is to get a CD of the numberator, get a CD of the denominator and then use these to build an overall CD. Now multiply every term by the factor missing from the overall CD and create a single RE and simply. I am going to use the same problem to illustrate Method 2 since we already know the answer to the problem.
Example Simplify the following complex fraction (Method 2):
$$\frac{\frac{1}{a}-\frac{1}{b}}{\frac{1}{a^2}-\frac{1}{b^2}}$$For some problems, Method 1 will be easier to do. For others, Method 2 may be best. The videos show that is does not really matter what method is used, both will arrive at the same answer. So select a method, and start to practice, practice, practice!