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What algebraic property can I use here?

  1. Oct 8, 2016 #1
    1. The problem statement, all variables and given/known data

    example problem: 5 = [(x)(4+x)] / (4-x)

    answer: 5

    2. Relevant equations
    Unsure what to use.

    3. The attempt at a solution

    Not sure what my professor did, but I thought that if i multiply by the reciprocal of something, I have to balance by multiplying the other side as well. It seems like everything just cancelled out and the only thing left was x = 5. I would just like to know what algebraic property or technique can be used to find x BESIDES quadratic formula.
     
  2. jcsd
  3. Oct 9, 2016 #2

    Simon Bridge

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    This is the purpose of taking notes in class.
    Yes.
    Do you mean that is your vague recollection of what the prof did or that is what happened when you did it?
    ...what's wrong with the usual rules for multiplication and addition?
    What was the topic of the class?

    Have you tried substituting the stated solution x=5 into the equation to see if it really is the solution?
    (I am guessing that "answer:5 means x=5 will make the expression true...)
     
    Last edited: Oct 9, 2016
  4. Oct 9, 2016 #3
    its for a general chemistry class, everything makes sense (as far as chemistry goes) up until that last step right before the answer. Not sure what you mean by rules for multiplication and addition.
     
  5. Oct 9, 2016 #4

    Simon Bridge

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    I am guessing that "answer:5" means that putting x=5 into the expression 5=[x(4+x)]/(4-x) will make it true.
    Have you tried this to see?

    Do you know how to add and how to multiply?
     
  6. Oct 9, 2016 #5

    Mark44

    Staff: Mentor

    If you add the same quantity to both sides of an equation, the new equation will have the same solutions as the original equation.
    If you multiply both sides of an equation by the same nonzero quantity, the new equation will have the same solutions as the original equation.
     
  7. Oct 9, 2016 #6

    Ray Vickson

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    Are you solving an equation of the form
    $$
    \frac{x(4+x)}{4-x} = 5 ?
    $$
    If so, x=5 has nothing to do with it: there are two solutions, which are obtainable from the quadratic solution formula: x ≈ -10.84 and x ≈ 1.84.
     
    Last edited: Oct 9, 2016
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