Simplifying Rational Functions with Factoring and GCFs - Problem 3

When you have a rational expression that you want to simplify your job is to factor completely factor the bottom completely and then look for any factors that are the same from top to bottom.

Here we go so on top I have a binomial where 8 is a common factor that’s the factored version of the top. On the bottom I know my first terms have to be 2m and m because those are the only things whose product is 2m and I know my second terms have to be 2 and 1, so I’m going to stick in there 2 and 1.

Now in my head I’m going to try Foiling and make sure I do have 5ms. My first work here’s 4m plus one more m that’s 5m good, plus 2. Okay for now I know I got that correctly factored.

The next step is just cancel out any factors that are exactly the same on top and bottom like that whole m plus 2 businesses. Now I’m left with 8/2m plus 1.

That’s my most simplified form don’t be tempted to reduce 8/2 because that 2 is not being multiplied by m plus 1 it's 2m then +1 that’s tricky again you can’t cancel out those things because 2 is not a factor on the bottom.

That is my most simplified form the other thing that I need to do is find any excluded values for this expression. Excluded values means it would make the expression undefined or it would make the denominator equal to 0.

So in order to find my excluded values I’m going to set my denominator equal; to 0and then solve for m. The way I would do that is by factoring, luckily I’ve already done that, I have 2m plus 1 and m plus 2 using the zero product property I have two different problem to solve 2m plus 1 equals 0 and m plus 2 equals 0 when I solve I see I have two excluded values.

I’ll have m equals -1/2 and m equals -2. Those are my excluded values so in fact I’m going to write m cannot be or m does not equal -1/2 and m does not equal -2.

That will show that these are the two excluded values these are the two m numbers that will make my original expression undefined. So this is a two step process just make sure you are keeping track of your work. Make sure you are factoring everything accurately and then keep track of what’s your excluded values as opposed to what’s your simplified expression.