1/(x+3)-1/(x-3)=3

1/(x+3)-1/(x-3)=3

$\begin{array}{|rcll|} \hline 3 &=& \frac{1}{x+3}-\frac{1}{x-3} \quad & | \quad \cdot (x+3)(x-3) \\ 3\cdot (x+3)(x-3) &=& \frac{ (x+3)(x-3)}{x+3}-\frac{ (x+3)(x-3)}{x-3} \\ 3\cdot (x+3)(x-3) &=& (x-3) - (x+3) \\ 3\cdot (x+3)(x-3) &=& x- 3 - x-3 \\ 3\cdot (x+3)(x-3) &=& -6 \quad & | \quad : 3 \\ (x+3)(x-3) &=& -2 \\ x^2-9 &=& -2 \quad & | \quad +9 \\ x^2 &=& 7 \quad & | \quad \text{square root both sides} \\ \mathbf{x} & \mathbf{=} & \mathbf{\pm\sqrt{ 7 } }\\ \hline \end{array}$