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Math Help - algebraic manipulation

  1. #1
    Newbie madmartigano's Avatar
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    algebraic manipulation

    I need to find the relationship between A and B, where

    A = \frac{{{L_2} - {L_1}}}{{{L_1}\left( {{t_2} - {t_1}} \right)}}<br />
and B = \frac{{{V_2} - {V_1}}}{{{V_1}\left( {{t_2} - {t_1}} \right)}}

    I'm assuming I need to make {V_1} = {L_1}{W_1}{H_1}\,\,\,{\rm{and}}\,\,\,{V_2} = {L_2}{W_2}{H_2}


    So basically, how do I get

    \frac{{{L_2} - {L_1}}}{{{L_1}\left( {{t_2} - {t_1}} \right)}} out of \frac{{{L_2}{W_2}{H_2} - {L_1}{W_1}{H_1}}}{{{L_1}{W_1}{H_1}\left( {{t_2} - {t_1}} \right)}} ?


    I've only gotten so far:

    {W_1}{H_1}B = \frac{{{L_2}{W_2}{H_2} - {L_1}{W_1}{H_1}}}{{{L_1}\left( {{t_2} - {t_1}} \right)}}

    and I can't figure out how to extract {{L_2} - {L_1}} from the numerator on the right side of the equation.

    Is this even possible? Am I going about this problem incorrectly?
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  2. #2
    Moo
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    Hello,

    Your initial question is to get a relation between A and B, right ?

    If so, just look at their formulas. They both have (t_2-t_1) in it.

    So, for example, write that t_2-t_1=\frac{V_2-V_1}{V_1B} and substitute it in A.

    If it's not what you're looking for, can you be more precise about what you want ? I can't see what you want to do with the stuff you've written down in the rest of your message
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  3. #3
    MHF Contributor
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    Or, if we divide A by B, we can invert B and multiply

    \frac{A}{B}=\frac{L_2-L_1}{L_1(t_2-t_1)}\ \frac{V_1(t_2-t_1)}{V_2-V_1}=\frac{V_1(L_2-L_1)}{(V_2-V_1)L_1}
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  4. #4
    Newbie madmartigano's Avatar
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    Thank you. I suppose I was just overthinking the problem. Got it now
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