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Thread: Simplifying algebraic fraction

  1. #1
    Newbie hymnseeker's Avatar
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    Simplifying algebraic fraction

    $\displaystyle \frac {x^2-5x-6}{x -1} = x - 4 - \frac {10}{x -1}$

    How to I achieve this simplification? So far I have:

    $\displaystyle \frac {(x-6)(x+1)}{x -1}$

    Am I on the right lines here?
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  2. #2
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    Hello, hymnseeker!

    $\displaystyle \frac {x^2-5x-6}{x -1} \;=\; x - 4 - \frac {10}{x -1}$

    How to I achieve this simplification?
    One way is long division . . .


    . . $\displaystyle \begin{array}{ccccc}
    & & & x & - 4 \\
    & & -- & -- & -- \\
    x-1 & ) & x^2 & -5x & -6 \\
    & & x^2 & -x \\
    & & -- & -- \\
    & & & -4x & -6 \\
    & & & -4x & +4 \\
    & & & -- & -- \\
    & & & & -10
    \end{array}$


    Therefore: .$\displaystyle \frac{x^2-5x - 6}{x-1} \;=\;x - 4 - \frac{10}{x-1} $

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  3. #3
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    That works, thank you Soroban.
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by hymnseeker View Post
    $\displaystyle \frac {x^2-5x-6}{x -1} = x - 4 - \frac {10}{x -1}$

    How to I achieve this simplification? So far I have:

    $\displaystyle \frac {(x-6)(x+1)}{x -1}$

    Am I on the right lines here?
    Hi hymnseeker,

    Another way is synthetic division. A very similar example is found at that link.

    Code:
       ______________
    1 | 1  -5  -6
            1  -4
       ----------------
        1  -4  -10
    Solution: $\displaystyle x-4-\frac{10}{x-1}$
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