Simplify algebraic expression with radicals: $\frac{1- ax}{1+ ax} \cdot \sqrt\frac{1+bx}{1-bx}$

Question

I got stuck trying to simplify this roots forest:

$\frac{1- ax}{1+ ax}*\sqrt\frac{1+bx}{1-bx}$

where x= $\sqrt{\frac{2a}{b}-1}$

So it is:

$\frac{1- a\sqrt{\frac{2a}{b}-1}}{1+ a\sqrt{\frac{2a}{b}-1}}*\sqrt\frac{1+b\sqrt{\frac{2a}{b}-1}}{1-b\sqrt{\frac{2a}{b}-1}}$

Answer 1

HINT: we get $$1-a\frac{\sqrt{2a-b}}{\sqrt{b}}=\frac{\sqrt{b}-a\sqrt{2a-b}}{\sqrt{b}}$$ for $b>0$ I have got the following result $$\frac{\sqrt{b}-a\sqrt{2a-b}}{\sqrt{b}+a\sqrt{2a-b}}\cdot \frac{\sqrt{1+\sqrt{b}\sqrt{2a-b}}}{\sqrt{1-\sqrt{b}\sqrt{2a-b}}}$$ if $$2a-b\geq 0$$