Resolver (a^{2}-b^2)x^2-4abx+b^2=a^2

$$( a ^ { 2 } - b ^ { 2 } ) x ^ { 2 } - 4 a b x + b ^ { 2 } = a ^ { 2 }$$

Resolva para a

$$\left\{\begin{matrix}a=\frac{b\left(x+1\right)}{x-1}\text{; }a=\frac{b\left(1-x\right)}{x+1}\text{, }&|x|\neq 1\\a=\frac{b\left(1-x^{2}\right)}{4x}\text{, }&b\neq 0\text{ and }|x|=1\\a\in \mathrm{R}\text{, }&b=0\text{ and }|x|=1\end{matrix}\right,$$

Resolva para b

$$\left\{\begin{matrix}b=\frac{a\left(x+1\right)}{1-x}\text{; }b=-\frac{a\left(1-x\right)}{x+1}\text{, }&|x|\neq 1\\b=\frac{a\left(x^{2}-1\right)}{4x}\text{, }&a\neq 0\text{ and }|x|=1\\b\in \mathrm{R}\text{, }&a=0\text{ and }|x|=1\end{matrix}\right,$$