calculate x: (a+x)/(1-a*x) + (a-x)/(1+a*x) = b
You asked:
Solve the equation \[\frac{a + x}{1 - a x} + \frac{a - x}{1 + a x} = b\] for the unknown \(x\).
MathBot Answer:
$$\begin{aligned}x &= \sqrt{- \frac{2 a - b}{a \left(a b + 2\right)}}\\x &= - \sqrt{- \frac{2 a - b}{a \left(a b + 2\right)}}\end{aligned}$$ and \(x \neq \frac{1}{a}, x \neq - \frac{1}{a}\)