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Algebra - make the assumption?

  1. Jul 28, 2013 #1
    ##\frac{6-2x}{x^2-9}\times\frac{15+5x}{4x}##

    ##\frac{2(3-x)}{(x-3)(x+3)}\times\frac{5(3+x)}{4x}##

    ##\frac{3-x}{x-3}\times\frac{5}{2x}##

    Now do I make the assumption that ##x\neq3## ?

    If I make the assumption that ##x\neq3## then ##-1\times\frac{5}{2x} = -\frac{5}{2x}##
     
  2. jcsd
  3. Jul 28, 2013 #2
    You started of with

    [tex]\frac{6-2x}{x^2-9}\times\frac{15+5x}{4x}[/tex]

    For this to be well-defined, you make the assumption there that ##x\neq -3, 0, 3##. So you make the assumption in the beginning instead of in the end.
     
  4. Jul 28, 2013 #3
    How can you tell before even starting the question that ##x\neq-3,0,3## ? It only became obvious to me once I got to the last section. Even still my main question was is it the right thing to do to make the assumption? Should I be doing this with all questions and just include where ##x\neq-3,0,3## along with my answer?

    Would an examiner be looking for these types of checks?
     
  5. Jul 28, 2013 #4
    You want to avoid dividing by ##0##. So the denominator shouldn't be ##0##. I see two denominators, namely ##x^2 - 9## and ##4x##. Neither should be ##0##. Now, solving things, we get that ##x^2 - 9 = 0## if and only if ##x=-3,3## and ##4x = 0## if and only if ##x=0##. So you don't want ##x=-3,0,3##.

    Yes, you should make the assumption. But you should make the assumption in the beginning.

    Yes.

    They should be looking out for these things.
     
  6. Jul 28, 2013 #5
    Ok thank you
     
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