Solve the equation to obtain such a result form;
Reduce[a x1 + x1^2 - a x2 - x2^2 - Log[x1] + Log[x2] == 0,
a] // Simplify
(*a\[Equal](-x1^2+x2^2+Log[x1]-Log[x2])/(x1-x2)||x1\[Equal]x2*)
How to obtain this form, that is, if a part can be omitted, it can be omitted
a == -x1 - x2 + (Log[x1] - Log[x2])/(x1 - x2)
want to get this result as following picture
expr = Solve[a x1 + x1^2 - a x2 - x2^2 - Log[x1] + Log[x2] == 0, a][[1, 1]]
Apart[expr, x1]
TeXForm @ %
$a\to \frac{\log (\text{x1})-\log (\text{x2})}{\text{x1}-\text{x2}}-\text{x1}-\text{x2}$
expr = First@
Solve[a x1 + x1^2 - a x2 - x2^2 - Log[x1] + Log[x2] == 0, a]
$\left\{a\to \frac{-\text{x1}^2+\log (\text{x1})+\text{x2}^2-\log (\text{x2})}{\text{x1}-\text{x2}}\right\}$
r1 = Log[a_] - Log[b_] :> Log[a/b];
r2 = Log[a_/b_] :> Log[a] - Log[b];
(expr /. r1 // Apart) /. r2
$\left\{a\to \frac{\log (\text{x1})-\log (\text{x2})}{\text{x1}-\text{x2}}-\text{x1}-\text{x2}\right\}$
Try this:
expr1 = Solve[a x1 + x1^2 - a x2 - x2^2 - Log[x1] + Log[x2] == 0,
a][[1, 1]];
a -> ((-x1^2 + x2^2 + Log[x1] - Log[x2])/(
x1 - x2) /. -x1^2 + x2^2 -> Factor[-x1^2 + x2^2] /.
x1 - x2 -> z // Expand) /. z -> x1 - x2
a -> -x1 - x2 + Log[x1]/(x1 - x2) - Log[x2]/(x1 - x2)
Have fun!
Solvedeletes full-dimension components, since it's less rigorous, as shown in current answers.Or@@And@@@Apply[Equal,Solve[{x^2+y^2==4,x==y}],{2}]converts toReduceform. $\endgroup$