Question 189602
You are correct. Here's the check




Checking {{{x=12}}}



{{{30/(x^2-9) = 2/(x-3)}}} Start with the given equation.



{{{30/(12^2-9) = 2/(12-3)}}} Plug in {{{x=12}}}



{{{30/(144-9) = 2/(12-3)}}} Square 12 to get 144



{{{30/135 = 2/9}}} Subtract



{{{2/9 = 2/9}}} Reduce. Since the equation is true, this verifies that {{{x=12}}} is a solution.



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Checking {{{x=3}}}



{{{30/(x^2-9) = 2/(x-3)}}} Start with the given equation.



{{{30/(3^2-9) = 2/(3-3)}}} Plug in {{{x=3}}}



{{{30/(9-9) = 2/(3-3)}}} Square 3 to get 9



{{{30/0 = 2/0}}} Subtract. Since division by zero is undefined, this means that {{{x=3}}} is NOT part of the domain. So it is NOT a solution.