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Math Help - steps to simplify equation

  1. #1
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    Nov 2011
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    Question steps to simplify equation

    I have the following that I want to solve for v.

    S = b - dv + r(b - dv) + c[b - dv + r(b - dv)] + t(b - dv + r(b - dv) + c[b - dv + r(b - dv)])

    I started by getting rid of the parentheses:

    S = b - dv + rb - rdv + cb - cdv + crb - crdv + tb - tdv + trb - trdv + tcb - tcdv + tcrb - tcrdv

    Then, I reordered the terms and combined some like so:

    S = b(1 + r + c + cr + t + tr + tc + tcr) - dv(1 - r - c - cr - t - tr - tc - tcr)

    I have a few more steps that I took, but am wondering if someone could show me a better way to simplify and solve.

    What I have so for is this, but I think I made a mistake along the way:

    v = S - b[1 + r + c(1 + r + t + tr) + t + tr] / -d[1 - r - c(1 - r - t - tr) - t - tr]

    Any guidance is appreciated.

    Thanks,
    Erik
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  2. #2
    MHF Contributor Amer's Avatar
    Joined
    May 2009
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    Jordan
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    Re: steps to simplify equation

    you can take a factor
    S = b -dv +r(b-dv)+ c( b-dv+r(b-dv)) + t(b-dv+r(b-dv)+c[b-dv+r(b-dv)])

    as you can see you can factor b-dv in all

     S = (b-dv)(1+r) + c((b-dv)(1+r))+t([b-dv](1+r)+c[(b-dv)[1+r]])

    now factor (b-dv)(r+1)

    S = (b-dv)(1+r)(1+c) + t((b-dv)(1+r)(1+c))

    S = (b-dv)(1+r)(1+c)(1+t) it is nice and clear
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