Answer
There is no solution to the given equation.
Work Step by Step
Factor the denominators.
$\frac{2}{x-3}-\frac{3}{x+3}=\frac{12}{\left( x-3 \right)\left( x+3 \right)}$
The variable \[x\] has a restriction, $x\ne 3$ and$x\ne -3$.
The LCD is$\left( x-3 \right)\left( x+3 \right)$.
Multiply both sides by the LCD to clear the fractions.
\[\begin{align}
& \left( x-3 \right)\left( x+3 \right)\left( \frac{2}{x-3}-\frac{3}{x+3} \right)=\left( x-3 \right)\left( x+3 \right)\left( \frac{12}{\left( x-3 \right)\left( x+3 \right)} \right) \\
& \left( x+3 \right)2-\left( x-3 \right)3=12 \\
& 2x+6-3x+9=12 \\
& -x+15=12
\end{align}\]
Subtracting $15$ from both sides:
$\begin{align}
& -x+15-15=12-15 \\
& -x=-3 \\
& x=3
\end{align}$
which is not possible as it contradicts to our restriction value.
So, there is no solution exist for given equation.
