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Math Help - all sorts of algebra questions

  1. #1
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    all sorts of algebra questions

    1. simplify



    2. If ,what does equal to?

    3.
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by masterwizard View Post
    1. simplify
     \frac{m}{m - n} + \frac{n}{n - m} = \frac{m}{m - n} - \frac{n}{m - n} = \frac{m - n}{m - n} = 1


    2. If ,what does equal to?
     a + b = 7 and  a - b = 4
     a = b + 4 Set this value into the first equation.
     b + 4 + b = 7
     b = 1,5

    Therefore  a = 5,5

    Now you'll be able to do  \frac{a^2}{b^2}

    3.
     \frac{1}{ab + b^2} + \frac{1}{ab + a^2} = \frac{1}{b(a + b)} + \frac{1}{a(a + b)} = \frac{a + b}{ab(a + b)} = \frac{1}{ab}
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  3. #3
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    Hello, masterwizard!

    #2 could be a dangerous problem . . .


    If . \frac{a+b}{a-b} = \frac{7}{4}, what does \frac{a^2}{b^2} equal?

    We should not assume that the fraction is already reduced to lowest terms.

    If . \frac{a+b}{a-b} has been reduced to \frac{7}{4},

    . . then we have: . \begin{array}{c}a + b \:=\:7k \\ a - b \:=\:4k\end{array} . . . for some integer k.

    Hence: . \begin{array}{c}a \:=\:\frac{11}{2}k \\ b\:=\:\frac{3}{2}k\end{array}

    Therefore: . \frac{a^2}{b^2}\;=\;\frac{\left(\frac{11}{2}k\righ  t)^2}{\left(\frac{3}{2}k\right)^2} \;=\;\frac{\frac{121}{4}k^2}{\frac{9}{4}k^2} \;=\;\frac{121}{9}


    We arrive at the same answer, but if we are required to show our work,
    . . janvdl's solution could lose some points.

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  4. #4
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    Well, I don't understand this part.
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  5. #5
    Bar0n janvdl's Avatar
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    Quote Originally Posted by masterwizard View Post
    Well, I don't understand this part.
    Look at what we are given:
     a + b = 7k

     a - b = 4k
    Add those 2 equations together and you'll get:

     a + a + b - b = 7k + 4k

     2a = 11k

     a = \frac{11k}{2}


    Subtract those 2 equations from each other and you'll get:

     a - a + b + b = 7k - 4k

     2b = 3k

     b = \frac{3k}{2}
    Last edited by janvdl; July 16th 2007 at 08:37 AM.
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