Solve frac{b^{2}(x^2/a^2-1)}{x^2-a^2}=1/3

$$\frac { b ^ { 2 } ( \frac { x ^ { 2 } } { a ^ { 2 } } - 1 ) } { x ^ { 2 } - a ^ { 2 } } = \frac { 1 } { 3 }$$

Solve for a (complex solution)

$$a=-\sqrt{3}b$$

$$a=\sqrt{3}b\text{, }b\neq -\frac{\sqrt{3}x}{3}\text{ and }b\neq \frac{\sqrt{3}x}{3}\text{ and }b\neq 0$$

Solve for b (complex solution)

$$b=-\frac{\sqrt{3}a}{3}$$

$$b=\frac{\sqrt{3}a}{3}\text{, }a\neq 0\text{ and }x\neq a\text{ and }x\neq -a$$

Solve for a

$$a=\sqrt{3}b$$

$$a=-\sqrt{3}b\text{, }b\neq 0\text{ and }|b|\neq \frac{\sqrt{3}|x|}{3}$$

Solve for b

$$b=\frac{\sqrt{3}a}{3}$$

$$b=-\frac{\sqrt{3}a}{3}\text{, }a\neq 0\text{ and }|x|\neq |a|$$