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So I've been working on a project, and hope to simplify the expression

enter image description here

by substituting the values

and

enter image description here

To obtain a polynomial in terms of the variable [$H^+$] only. Note that I understand this question borders on Chemistry, but the way to arrive at the required equation is based off mathematical manipulation.

After substituting the values of [$A^-$], [$B^+$] and [$OH^-$] in the first equation, I'm left with a very complicated equation that I have no clue what to do with. Any help/ suggestions/starting points?

PS: Here are the expressions that might help:

enter image description here

Thanks!

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    After the substitutions multiply by the product of denominators and simplify. Then distribute the products and put everything on one side. – 2017-01-04

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It might be helpful to nondimensionalize your equation. I would recommend doing this before plugging everything in because it might get messy otherwise.

To nondimensionalize something you can use the buckingham pi theorem (more systematic) or you can make the following change of variables for each quantity which is not a constant: x=x'x_c where x_c is a constant with the desired dimensions of x and x' is a dimensionless variable. Once you make that substitution you can often simply things to reduce it to less variables than you originally had.

My other suggestion is if you have access to Mathematica (or maybe wolfram alpha) plug your result into the simplify function and see if that helps.