This week in Precalc 11 we worked on solving rational expressions by multiplying and dividing and we also learned how to write the non-permissible values.

We first started off by simplifying radical expressions. When you are given an expression the first thing that you want to do is look if you can factor anything on the top or on the bottom. Once you factor it, you look for any similarities between the numerator and the denominator. Then you can then cross them off because it is equal to 1 or of you see a fraction that can be reduced you can do the as well. After you have finished simplifying it you have to write the non-permissible values. How you do that, you have to look at the original equation and figure out what values for x would result in the denomination to equal zero.

Here is an example:

If you are given radical expressions that you need to multiply, you would do the same steps that you do to simplify.

If this was your equation:

The first thing that you would do is notice that there is no factoring that needs to be done. Now I noticed that there is a (x-3) on the top and the bottom, meaning I can just cross it off because it equals 1.

Now you may notice the the 8 and the 2 both have something in common meaning you can divide then both, in this case you can divid them both by 2, so now there is a 4 at the top and 1 at the bottom.

The 3x and the 9x^2 also have something in common, 3x so you can divide the top and bottom by 3x, leaving you with 1 x 4 on the top and 1 x 3x at the bottom.

After you have it simplified, you are not done yet, you still have to write the non-permissible values. If you look at the original question you can see that there can’t be a 0 for x or a 3 so those would be your values and your final answer will look like this: