Rational Expressions!
A big word that really isn’t that bad. We’ve been doing simple rational expressions since grade 9, we just didn’t know it yet. Now, however, they are getting a bit more in-depth.
All a rational expression is is an expression that has a polynomial in the numerator or the denominator. As I said, we did this on a very basic level in grade 9 with very simple expressions that already had like denominators. All that means is the same number was already on the bottom.
This is incredibly important when working with rational expressions. You can think of it like working with fractions. To add or subtract fractions, you need to have like denominators. The only difference is we have some variables and more than just one number.
Another similarity to simple fractions is the “what happens to the top happens to the bottom rule.” Anything you to the top/bottom needs to happen vice-versa.
Let’s start with a really simple expression.
I found the lowest common denominator then applied each multiplication to the top and bottom of each fraction.
Here is a bit more difficult expression that uses binomials
- First off, the find the LCD, I need to multiply the two denominators together in their respective fractions. Going back the “top/bottom” rule, that means I have to multiply the numerator by the same amount.
- Now I let algebra take over and multiply out the numerators
- Since I have like denominators, I can put everything over one denominator because they are the same.
- After simplifying as much as possible, you have an answer.
- *** Note that you do not multiply out the bottom factored expression. That just makes things more confusing.
One final golden rule is that a + and a – symbol are like the glue of the expression. When to numbers have this in between them, they cannot be pulled apart individually. It makes it a package product.
That’s all for this week!