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Math Help - Algebraic fraction?

  1. #16
    MHF Contributor MarkFL's Avatar
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    Re: Algebraic fraction?

    Quote Originally Posted by Ashir View Post
    Why did you do that?
    Where did x+1 come from?
    Why both numerator and denominator?
    Why can't we just treat it as a normal fraction?
    Why wasn't my method correct? Or was it?
    What do you mean 'foil'?
    What do you mean by distribute?
    1.) The x+1 comes from:

    \frac{(x+1)(x-1)}{x-1}=x+1

    More simply, we see that the denominator in the first term needs the factor x+1 to be equal to the denominator in the second term.

    2.) You have to multiply both the numerator and the denominator by the same thing so that in effect you are multiplying the term by 1, and so its value remains unchanged.

    3.) What do you mean by normal fraction?

    4.) No, your method was not correct.

    5.) FOIL is an acronym used as a mnemonic device for multiplying binomials. If you have:

    (a+b)(c+d) you can find the product from the sum of:

    F: product of "first" terms or ac
    O: product of "outer" terms or ad
    I: product of "inner" terms or bc
    L: product of "last" terms or bd

    Hence:

    (a+b)(c+d)=ac+ad+bc+bd

    6.) To distribute essentially means:

    a(b+c)=ab+ac

    The term on the outside is "distributed" to the terms on the inside.
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  2. #17
    Junior Member alane1994's Avatar
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    Re: Algebraic fraction?

    Does it make any sense now?
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  3. #18
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    Re: Algebraic fraction?

    Not at all I'm afraid. My teacher can do it much easier but she only has so much time
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  4. #19
    MHF Contributor MarkFL's Avatar
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    Re: Algebraic fraction?

    I can guarantee you that your teacher is finding the lowest common denominator, then combining the terms and simplifying.

    The only thing easier is explaining the process in person rather than online.
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  5. #20
    Junior Member alane1994's Avatar
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    Re: Algebraic fraction?

    Quote Originally Posted by MarkFL2 View Post
    I can guarantee you that your teacher is finding the lowest common denominator, then combining the terms and simplifying.

    The only thing easier is explaining the process in person rather than online.
    On the nose my friend...
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  6. #21
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    Re: Algebraic fraction?

    Quote Originally Posted by Ashir View Post
    2x/x-1 - 7x-3/x^2-1
    \frac{2x}{x-1}-\frac{7x-3}{x^2-1}

    \frac{2x(x+1)-(7x-3)}{x^2-1}

    \frac{2x^2-5x+3}{x^2-1}

    \frac{(2x+1)(x-3)}{x^2-1}
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  7. #22
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    Re: Algebraic fraction?

    Quote Originally Posted by Plato View Post
    \frac{2x}{x-1}-\frac{7x-3}{x^2-1}

    \frac{2x(x+1)-(7x-3)}{x^2-1}

    \frac{2x^2-5x+3}{x^2-1}

    \frac{(2x+1)(x-3)}{x^2-1}
    Almost got it. Why did x^2-1 remain the denominator and why did 2x become 2x(x+1)
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  8. #23
    Junior Member alane1994's Avatar
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    Re: Algebraic fraction?

    Because, like I told you you multiply both the numerator and denominator by x+1...
    x^2-1 remained in the denominator because it is the least common denominator...
    Not to be rude, but you need to brush up on your basic fraction mathematics. You can't do this level if you don't have a firm grasp on fractions with just numbers...
    Tell me what these would equal.

    1)\frac{8}{5}+\frac{3}{7}=

    2)\frac{1}{6}-\frac{7}{9}=

    3)\frac{5}{8}\times\frac{2}{5}=

    4)\frac{3}{7}\div\frac{9}{13}=
    Last edited by alane1994; October 11th 2012 at 06:00 AM.
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  9. #24
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    Re: Algebraic fraction?

    Quote Originally Posted by alane1994 View Post
    Because, like I told you you multiply both the numerator and denominator by x+1...
    x^2-1 remained in the denominator because it is the least common denominator...
    Not to be rude, but you need to brush up on your basic fraction mathematics. You can't do this level if you don't have a firm grasp on fractions with just numbers...
    Tell me what these would equal.

    1)\frac{8}{5}+\frac{3}{7}=

    2)\frac{1}{6}-\frac{7}{9}=

    3)\frac{5}{8}\times\frac{2}{5}=

    4)\frac{3}{7}\div\frac{9}{13}=
    I'll just do the first one to show I can, don't have time to do the rest.
    56/35 + 15/35 = 71/35 = 2 1/35
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