Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    so

    -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)

    [tex]\frac{-5x}{2\sqrt{(x+3)^3}}+\frac{5}{\sqrt{x+3}}[/tex]

    [tex]\frac{-5x}{2(x+3)\sqrt{x+3}}+\frac{5}{\sqrt{x+3}}[/tex]

    [tex]\frac{-5x+5*2(x+3)}{2(x+3)\sqrt{x+3}}[/tex]

    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)

    simplify

    10x+30

    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.

    Regards.
     
  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

    [tex]\frac{\frac{-4x}{x(x+h)}+\frac{-4(x+h)}{x(x+h)}}{h}[/tex]

    [tex]\frac{-4x-4x-4h}{xh(x+h)}[/tex]

    The final result:

    [tex]-\frac{4(2x+h)}{xh(x+h)}[/tex]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook