1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Rational expressions and domains

  1. Nov 1, 2017 #1
    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) x2 + 6x +5 / x2 - 25
    b) x-7 / x-1 multiplied by x2-1 / 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?
     
  2. jcsd
  3. Nov 1, 2017 #2

    DoItForYourself

    User Avatar
    Gold Member

    Yes, this is the way it works.

    You can understand why, if you calculate the result of (x2+6x+5)/(x2-25) if you put x=-5.
     
  4. Nov 1, 2017 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    In both (a) [##x^2 + 6x + \frac{5}{x^2} - 25##] and (b) [##x = \frac{7}{x} -1##] only the point ##x=0## is excluded. Or, maybe, you did not write what you actually meant, in which case you should re-write the expressions to say what you mean. The expression "a + b/c + d" means ##a + \frac{b}{c} + d## when parsed according to official math rules. If you mean ##\frac{a+b}{c+d}## then you need to either use LaTeX (as I have just done) or else use parentheses, like this" "(a+b)/(c+d)".
     
  5. Nov 1, 2017 #4

    Mark44

    Staff: Mentor

    As Ray mentioned, you need more parentheses. In the first quote above, your first expression isn't correct, even with your use of parentheses. It would be interpreted as ##(x + 5) \frac{x+1}{x + 5} (x - 5)##, which is surely not what you meant. A better way to write it on one line would be [(x+5)(x+1)] / [(x+5)(x-5)], so now it's clear which factors are in the numerator and which are in the denominator. As alread mentioned, expressions like x + 1 / x -5 aren't the same as (x + 1)/(x - 5).
    Same comments on the second quote.
     
  6. Nov 3, 2017 #5
    Hey, thanks for the replies. Yes, everything was in parenthesis but I didn't write it like that in the post. I will do so in the future.
     
  7. Nov 4, 2017 #6

    scottdave

    User Avatar
    Homework Helper
    Gold Member

    Another thing to take away from this: you cannot "cancel out" expressions which equal zero. You cannot have zero divided by zero
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Rational expressions and domains
  1. Rational Expression (Replies: 2)

  2. Rational Expressions (Replies: 3)

Loading...