Rational expression questions

Question

Premise: the first two questions were to simplify ((1/x+3)+(6/x^2+4x+3))*(x+3)/(x+1), and then explain how I got there (which I did). I got the answer of (x+7)/(x+1)^2. The questions I am not sure how to answer are the following:

• Are there any values "x" cannot be? Explain.

• Find the values of "x" that make the expression equal to 0. Explain the steps you would use to find these values.

Any help is appreciated!

Answer 1

Remember, that you cannot divide by 0. So set the denominator = 0 and solve. Those will be the values that will make the expression undefined.

Similarly, set the numerator to 0 and solve. That will give you the values which will make the expression equal to 0.