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Math Help - Review Problems (Test Tommorow)

  1. #1
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    Review Problems (Test Tommorow)

    I've been reviewing all day for a test tommorow and the following are the problems I have no idea how to complete. I don't expect them all to be answered but any help/explanation would be greatly appreciated.

    1) Simplify the expression.
    \frac{3(1+x)^1/^3-x(1+x)^-2/^3}{(1+x)^2/^3}

    ^Sorry about the messed up exponents.

    2) Find all real solutions to the equation.
    \frac{x+5}{x-2}=\frac{5}{x+2}+\frac{28}{x^2-4}

    Thanks.
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  2. #2
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    Quote Originally Posted by Ballplaya4237 View Post
    I've been reviewing all day for a test tommorow and the following are the problems I have no idea how to complete. I don't expect them all to be answered but any help/explanation would be greatly appreciated.

    1) Simplify the expression.
    \frac{3(1+x)^1/^3-x(1+x)^-2/^3}{(1+x)^2/^3}

    ^Sorry about the messed up exponents.

    2) Find all real solutions to the equation.
    \frac{x+5}{x-2}=\frac{5}{x+2}+\frac{28}{x^2-4}

    Thanks.
    for the first one, i couldnt really understand, but i can give you tip to replace (1+x) with a variable, and it'll look a lot cleaner, then sub it back in at the end.

    im kinda busy so for the second ill just tell you that u need restrictions from the denominators at the end, for ex. x=/=-5 because it would make that first fraction divided by zero.
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  3. #3
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Ballplaya4237 View Post
    2) Find all real solutions to the equation.
    \frac{x+5}{x-2}=\frac{5}{x+2}+\frac{28}{x^2-4}

    Thanks.
    (x^2 - 4) = (x - 2)(x + 2)

    Multiply straight through with (x - 2)(x + 2)

    Then you get:

    (x+5)(x+2) = (5)(x-2)+28

    x^2 + 7x + 10 = 5x - 10 + 28

    x^2 + 7x - 5x -28 = 0

    x^2 + 2x -28 = 0

    x = 4,3851...

    OR

    x = -6,3851...


    ---

    Still working on the first one.
    Last edited by janvdl; January 27th 2008 at 10:11 PM. Reason: Messed up with a neg sign
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  4. #4
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Ballplaya4237 View Post
    1) Simplify the expression.
    \frac{3(1+x)^1/^3-x(1+x)^-2/^3}{(1+x)^2/^3}
    Let (1 + x)^{ \frac{1}{3} } = y

    = \frac{ 3y - xy^{-2} }{ y^2 }

    = \frac{ y(3 - xy^{-3}) }{ y(y) }

    = \frac{ (3 - xy^{-3}) }{ (y) }

    Now set y = (1 + x)^{ \frac{1}{3} } back into the equation.

    ---

    Good luck with the test.
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