Rewrite \({x}^{2}-9\) in the form \({a}^{2}-{b}^{2}\), where \(a=x\) and \(b=3\).
\[\frac{{x}^{2}-{3}^{2}}{x-3}=6\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[\frac{(x+3)(x-3)}{x-3}=6\]
Cancel \(x-3\).
\[x+3=6\]
Subtract \(3\) from both sides.
\[x=6-3\]
Simplify \(6-3\) to \(3\).
\[x=3\]
Check solution
When \(x=3\), the original equation \(\frac{{x}^{2}-9}{x-3}=6\) does not hold true.We will drop \(x=3\) from the solution set.
Therefore,
[No Solution]
