Compare two expressions in term of one variable

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I am trying to compare below two expressions:



$$E_1 = sum_iW^1_ifrace^W^2_ix-e^-W^2_ixe^W^2_ix+e^-W^2_ix quad E_2 = sum_iW^1_ifrace^W^3_ix-e^-W^3_ixe^W^3_ix+e^-W^3_ix$$



where $W^1,W^2$ and $W^3$ are known real numbers and $x$ is unknown real number. I am trying to find a way to compare $E_1$ and $E_2$ such that $x$ can be taken out as a function for example :



$$h(E_1,E_2) = f(W^1,W^2,W^3) + g(x)$$



where $h(E_1,E_2)$ can be $E^1 - E^2$. I would be really grateful if someone can give pointers on how to approach the problem.







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    I am trying to compare below two expressions:



    $$E_1 = sum_iW^1_ifrace^W^2_ix-e^-W^2_ixe^W^2_ix+e^-W^2_ix quad E_2 = sum_iW^1_ifrace^W^3_ix-e^-W^3_ixe^W^3_ix+e^-W^3_ix$$



    where $W^1,W^2$ and $W^3$ are known real numbers and $x$ is unknown real number. I am trying to find a way to compare $E_1$ and $E_2$ such that $x$ can be taken out as a function for example :



    $$h(E_1,E_2) = f(W^1,W^2,W^3) + g(x)$$



    where $h(E_1,E_2)$ can be $E^1 - E^2$. I would be really grateful if someone can give pointers on how to approach the problem.







    share|cite|improve this question
























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      I am trying to compare below two expressions:



      $$E_1 = sum_iW^1_ifrace^W^2_ix-e^-W^2_ixe^W^2_ix+e^-W^2_ix quad E_2 = sum_iW^1_ifrace^W^3_ix-e^-W^3_ixe^W^3_ix+e^-W^3_ix$$



      where $W^1,W^2$ and $W^3$ are known real numbers and $x$ is unknown real number. I am trying to find a way to compare $E_1$ and $E_2$ such that $x$ can be taken out as a function for example :



      $$h(E_1,E_2) = f(W^1,W^2,W^3) + g(x)$$



      where $h(E_1,E_2)$ can be $E^1 - E^2$. I would be really grateful if someone can give pointers on how to approach the problem.







      share|cite|improve this question














      I am trying to compare below two expressions:



      $$E_1 = sum_iW^1_ifrace^W^2_ix-e^-W^2_ixe^W^2_ix+e^-W^2_ix quad E_2 = sum_iW^1_ifrace^W^3_ix-e^-W^3_ixe^W^3_ix+e^-W^3_ix$$



      where $W^1,W^2$ and $W^3$ are known real numbers and $x$ is unknown real number. I am trying to find a way to compare $E_1$ and $E_2$ such that $x$ can be taken out as a function for example :



      $$h(E_1,E_2) = f(W^1,W^2,W^3) + g(x)$$



      where $h(E_1,E_2)$ can be $E^1 - E^2$. I would be really grateful if someone can give pointers on how to approach the problem.









      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Aug 9 at 19:43

























      asked Aug 9 at 16:54









      Dushyant Sahoo

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