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Algebra equivalence help

  1. Feb 10, 2014 #1
    Hi guys,

    please could someone tell me how this is equivalent and/or what the algebraic rule is?

    how is this: a/as + 1

    is equivalent to this: 1/s+1/a

    Thanks a lot for your time and help
  2. jcsd
  3. Feb 10, 2014 #2
    So a/as=1/s do you agree?
  4. Feb 10, 2014 #3


    Staff: Mentor

    First off, what you wrote is ambiguous. Taken literally, what you wrote is ##\frac{a}{a}s + 1 = s + 1##, if a ≠ 0.

    Assuming that's not what you meant, it could be either
    ##\frac{a}{as} + 1##
    or ##\frac{a}{as + 1}##

    Starting with 1/s + 1/a, the rule for adding fractions says that we need a common denominator, so
    1/s + 1/a = a/(as) + s/(as) = (a + s)/(as). This doesn't match any interpretations of what you wrote, so I don't see that what you started with is equal to 1/a + 1/s.
  5. Feb 10, 2014 #4
    Thanks for the replies. Sorry for the ambiguity i should have used parentheses.

    Mark44 - What i meant: how is a/(as+1) equivalent to 1/(s+(1/a))

    Me_student - i understand a/as=1/s but i dont understand how the other
    terms equal? i.e. how does the +1 term from a/(as+1) become 1/a?

    many thanks
  6. Feb 10, 2014 #5


    Staff: Mentor

    a/(as + 1) = a/[a(s + 1/a)]
    Can you finish it and show that the last expression is equal to 1/(s + 1/a)?
    What I did was factor a from both terms in the denominator.
    I explained that above.
  7. Feb 11, 2014 #6
    Thanks a lot Mark44 you've made that perfectly clear to me, i can see how the expressions equal now. Much appreciated :)
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