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Please help with this question:
Given that my page has
<divid="mathdiv">\[{3 x^2 + 4 x + 5}\]</div>
I learned from the MathJax site that I can change this equation dynamically. However, I wonder if it is possible to change each item, the coefficients, the operators, the unknown ... etc individually when clicked or touched on touch devices?
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Fred is right that MathJax doesn't currently provide an API to change individual elements within an equation. (It would be possible to modify the internal Element Jax tree and ask MathJax to rerender the result, but you are probably better off just replacing the entire equation and rerendering, as the parsing of the equation is not the time-consuming part of MathJax.)
On the other hand, perhaps you can use the <maction actiontype="toggle"> to accomplish what you need. When a user clicks on this element, it cycles through a list of expressions to display. There is an extension to give you access to this from within TeX. Add "action.js" to the extensions array in the TeX section of your configuration, and then you can use
\toggle{math1}{math2}...\endtoggle
to produce an expression initially showing math1, but when you click on "math1" it will change to "math2", and so on. So
x + \toggle{y}{\color{red}{y}} + z
would produce an equation where when you click on the y it turns red (and clicking again makes it black again). Perhaps that can do what you need.