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Math Help - Factorising

  1. #1
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    Factorising

    I need help factorising..

    Nk+1 = Nk + rNk(1-Nk/k)

    = (1+r -Nk/k)Nk

    Apparently that equals..

    = (1+r)[1-Nk/(1+r)k]Nk

    But i dont see how...
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  2. #2
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    Quote Originally Posted by dankelly07 View Post
    I need help factorising..

    Nk+1 = Nk + rNk(1-Nk/k)

    = (1+r -Nk/k)Nk

    Apparently that equals..

    = (1+r)[1-Nk/(1+r)k]Nk

    But i dont see how...
    N_k + r N_k \left(1 - \frac{N_k}{k} \right)


    = N_k \left[ 1 + r \left(1 - \frac{N_k}{k} \right) \right]


    = N_k \left[ 1 + r - \frac{r N_k}{k} \right]


    = N_k \left[ (1 + r) - \frac{r N_k}{k} \right]


    = N_k (1 + r) \left[1 - \frac{{\color{red}r} N_k}{k (1 + r)} \right]
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