(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Okay, I have two examples that are confusing me. I am not sure where all the numbers that must be excluded from the denominators so that we're not dividing by zero are coming from.

a) x^{2}+ 6x +5 / x^{2}- 25

b) x-7 / x-1 multiplied by x^{2}-1 / 3x-21

2. Relevant equations

None

3. The attempt at a solution

In a) I factor everything and get (x+5)(x+1) / (x+5)(x-5) and I am left with x+1 / x-5. I know that x cannot be 5, because 5-5=0 and division by zero is undefined. The text is saying that x cannot be -5 as well and I am confused. After factoring and before eliminating common factors, I have an x+5 where if x = -5, I would have 0...is that where the -5 is coming from? Do I consider all x values in the binomials before removing common factors?

In b) after factoring I am left with x-7 / x-1 multiplied by (x+1)(x-1) / 3(x-7). I canceled the x-7 terms and x-1 terms and I am left with x+1 / 3. The text is telling me that x cannot be 1, 7, which is confusing because I eliminated the common factors already.

I guess as I type this out it is making sense...I suppose at this point now that I have typed all this out I would like confirmation if someone could be so kind. It seems like all the x values to be excluded are taken from the binomials in the denominators before I eliminate common factors?

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# Homework Help: Rational expressions and domains

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