This week we finished our unit on Absolute Value and Reciprocal Functions and we started our unit on “Rational Expressions and Equations.” I enjoyed the unit on Absolute Value Functions because even though we continued on with graphing, it was still different than any unit we’ve done before and learning about asymptotes was so interesting to me because I’ve never seen anything like it before so I found that lesson very intriguing.
So far this week, we’ve only got through one lesson this unit and our first lesson was, “Equivalent Rational Expressions.” It was a pretty simple lesson considering it was the first one but it was also interesting. This unit, we don’t graph anything so we’re taking a break from the past few lessons we’ve had in graphing equations and different functions.
We reviewed that a rational number is a quotient of two integers and that the quotient of two polynomials is called a rational expression. This unit, we are expanding on our previous knowledge on factoring. An interesting example that we’ve been shown was comparing two fractions, the interesting part that we didn’t notice was that the two fractions were equivalent, I had no idea, basically for each fraction we had to find the value of x and for the given number, each fraction came out with the same number. What I noticed at the end was that one fraction was the original and the other one was the factored and simplified version of the first fraction. I also noticed that each value is equivalent for the two rational expressions because they are two forms of a rational expression (one factored and one not).
To reduce a rational expression, you first have to factor the numerator and denominator, and then cancel (divide) out the common factor. But then you have to make sure to find the non-permissible values BEFORE reducing the fraction otherwise you might make mistakes after factoring. Non-Permissible values are values that cause the denominator to equal 0 and that is not allowed in math, no number can divide by 0.
Here is an example: