Solve x^2-2b-b/(x-b)(x+b)=2x^2/b(x-b)(x+b)

$$\frac { x ^ { 2 } - 2 b - b } { ( x - b ) ( x + b ) } = \frac { 2 x ^ { 2 } } { b ( x - b ) ( x + b ) }$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{\sqrt{x^{2}\left(x^{2}-24\right)}+x^{2}}{6}\text{, }&x\neq 0\text{ and }x\neq 5\text{ and }x\neq -5\\b=\frac{-\sqrt{x^{2}\left(x^{2}-24\right)}+x^{2}}{6}\text{, }&x\neq 0\end{matrix}\right.$$

Solve for x (complex solution)

$$x=-\sqrt{3}\left(b-2\right)^{-\frac{1}{2}}b$$

$$x=\sqrt{3}\left(b-2\right)^{-\frac{1}{2}}b\text{, }b\neq 5\text{ and }b\neq 0\text{ and }b\neq 2$$

Solve for b

$$\left\{\begin{matrix}b=\frac{x\left(\sqrt{x^{2}-24}+x\right)}{6}\text{, }&x\leq -2\sqrt{6}\text{ or }\left(x\neq 5\text{ and }x\geq 2\sqrt{6}\right)\\b=\frac{x\left(-\sqrt{x^{2}-24}+x\right)}{6}\text{, }&\left(x\neq -5\text{ and }x\leq -2\sqrt{6}\right)\text{ or }x\geq 2\sqrt{6}\end{matrix}\right.$$

Solve for x

$$x=\sqrt{\frac{3}{b-2}}b$$

$$x=-\sqrt{\frac{3}{b-2}}b\text{, }b>2\text{ and }b\neq 5$$