Adding and Subtracting Rational Expression - Problem 1

These 2 rational expressions need to be added together, but I know it’s not going to be too bad because they already have common denominators. If I look both of these fractions already have x plus 2 in the bottom that means I know my sum is going to have x plus 2 in the bottom and all I need to do is look at the numerators or the tops.

It’s going to look like 3x² plus 6x. In order to simplify completely I’m going to factor the top and see if anything is going to cancel out and look my x plus 2 factors do cancel out, so my final sum is just going to be 3x.

The last thing I want to leave you with before you guys work on your homework problem though is that you have to consider excluded values. An excluded value remember is any value of x that would make this sum undefined, or what we mean by that is that would make this have a denominator of 0.

If I have the value x equals -2 that would mean my denominator would be 0 and in Math you guys know thou shall not divide by 0. 0 in the bottom of a fraction is what we call undefined. So I have the excluded value -2. I would write that as x cannot be -2 and I got that from looking at my original fractions, looking at the denominators and thinking about what values of x would make those denominators equal to 0.