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Homework Help: Adding fractions and evaluating functions

  1. Feb 8, 2010 #1
    1. The problem statement, all variables and given/known data
    1.) (a + 3b) /3ab + (a^2 b - 4ab^2) / 5a^2b^2

    2.) n/(m^2) + 3/mn + 2/m

    3.) Given F(x) = square root of x + 9 determine F(x+h) - F(x)/h

    4.) say whether or not {(x,y) l x= y^2} is a function.

    2. Relevant equations

    3. The attempt at a solution

    im having problems to find the least common multiple of the algebric expresions in the first two problems.

    I think that on problem one the LCM is 15 a^2 b^2

    I think that on the second problem the LCM is m^2 (mn) Is this right?

    On problem 3 I dont know how to solve (square root of(x+h) +9 - square root of x+9)/ h

    How can I solve that? should I use the square root's conjugate? and if so which is it?

    Thanks a lot.
  2. jcsd
  3. Feb 8, 2010 #2
    You're correct about the LCM for problem 1. Recheck what you got for problem 2. You are very close. You have an extra term in it.
  4. Feb 8, 2010 #3


    Staff: Mentor

    That's not the least common multiple. The LCM is m2n. Notice that all three denominators divide this evenly.
    Multiply by 1 in the form of the conjugate over itself. I can't tell you any more because what you wrote is ambiguous. Is it f(x) = sqrt(x + 9) or sqrt(x) + 9?
    You didn't ask about 4, but you included it. Graph the relation. If it's a function, no two points will be on the same vertical line.
  5. Feb 8, 2010 #4
    I ve done the first 2 problems.

    On problem 3 I meant sqrt(x + 9) sorry.
    Is the conjugate of problem 3 sqrt(x + h + 9) + sqrt(x+9) ?

    on problem 4 I considered that x = y^2 could be seen as sqrt x = y which is a function however in the book it said that problem 4 wasent a function. So im a bit confused about it.
  6. Feb 8, 2010 #5


    Staff: Mentor

    For 3, multiply your expression by 1 in the form of [sqrt(x + h + 9) + sqrt(x+9)] over itself.

    For 4, x = y2 <==> y = +/-sqrt(x). Now do you understand your book's answer?
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