Simplifying Rational Functions with Factoring and GCFs - Problem 1

This is a rational expression fraction that needs to be simplified so what I’m going to do is cross out any factors I have in the numerator and the denominator that are exactly the same.

One thing you might notice is that 4/16 can be reduced to ¼. So the start of my reduced version is going to be ¼. I’m also going to reduce x to the third on top if x by thinking of it like this, x to the third on top of x those guys get cancelled out and on top I just have x². So my final answer here is going to be x² over 4 that’s the reduced version of that original fraction. First I reduced the constants to ¼ then I reduced the x terms. 3x is on top 1 on the bottom.

Okay the last thing it asked me to do is to find the excluded values. Remember excluded values are values of x that would make this undefined or values of x that would make this have a denominator equal to 0.

So looking just at my denominator there’s only one number that x could be that would make that equal to 0 and that number is 0. If x were 0 here this would be undefined so this is my excluded value, x cannot be equal to 0 x could be any other number I want to on the whole planet. It just can’t be 0.