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Homework Help: Advanced Algebra, factor and simplify

  1. Jan 12, 2009 #1
    I am having problems understanding this. Could someone explain how to arrive at the answer for this problem .

    (-5/2)(x)(x+3)^(-3/2) + (5)(x+3)^(-1/2)

    Thank you

    It says to factor and simplify. Express the answer as a fraction without negative exponents.

    This is where I get to

    (-5x/2)(1/cubed root of (x+3)^3) + 5 / (cubed root of x+3 )

    edit here is more i got

    -5x/2(x+3)^2) + 5/(x+3)

    get common denominator times the second by x+3 then by 2


    -5x/2(x+3)^2 + 10x + 30 / 2(x+3)^2

    I assume I have to get a common denominator but I am unsure of how to do that with negative fraction exponents that are not already equal.
    Last edited: Jan 12, 2009
  2. jcsd
  3. Jan 12, 2009 #2
    (-5/2)(x)(x+3)^(-3/2) + (5)(x+3)^(-1/2)




    Do you feel comfortable to continue now?
  4. Jan 12, 2009 #3
    let me try now

    attain common denominator

    so multiply other side by 2(x+3)

    so we get

    -5x/2(x+3)(square root x+3) + 10(x+3)/2(x+3)(square root x+3)



    since they are know common denominators do the addition

    5x + 30 / 2x+6(square root x+3)

    Is this correct or am I wrong ?
  5. Jan 12, 2009 #4
    You're right. Also, it is even better when you rationalize (multiply the whole equation with sqrt(x+3)/sqrt(x+3)) so that you eliminate the square root in the denominator.

  6. Jan 12, 2009 #5
    thank you very much aaron you really helped me out with future problems. Our teacher said only 25% of students pass this class out of 24.

    Here is my next one I tried to work

    ((-4/x+h) + (-4/x) ) / h

    I remember something called ltw, where if you had addition in the denominator you multipled each side by the others denominator.

    So we would get

    -4x/(x^2 + h) + 4x + h / x^2 + h

    of course all divided by h

    now that the top has a common denominator we simplay add the two together leaving us

    h / x^2 + h the H should cancel out leaving

    1/ x^2

    now for the remainder the total problem is now

    (1/x^2) / h we can reverse the bottom and multiply fractions so

    1/(x^2) * 1/h

    we get

    1/ (x^2H)

    is this correct Aaron?

    btw you are really smart. :)
  7. Jan 12, 2009 #6
    When you multiply the denominator x + h by x how do you end up with x^2 + h?
  8. Jan 13, 2009 #7
    ((-4/x+h) + (-4/x) ) / h



    The final result:

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