Question 833098
Let's assume it's true for all values of {{{a}}} and {{{b}}} given neither {{{a}}} nor {{{b}}} equal zero.
{{{a/b-b/a=(a-b)/(ab)}}}
Multiply both sides by {{{ab}}},
{{{a^2-b^2=a-b}}}
{{{(a+b)(a-b)=a-b}}}
{{{a+b=1}}}
So the statement does not hold for all values of {{{a}}} and {{{b}}}.
It only holds when {{{a+b=1}}} which violates our initial assertion that it holds for all values of {{{a}}} and {{{b}}}, so then it is not true.