<s>[INST] Simplify algebraic expression with radicals: $\frac{1- ax}{1+ ax} \cdot \sqrt\frac{1+bx}{1-bx}$ 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:   
$\frac{1- a\sqrt{\frac{2a}{b}-1}}{1+ a\sqrt{\frac{2a}{b}-1}}*\sqrt\frac{1+b\sqrt{\frac{2a}{b}-1}}{1-b\sqrt{\frac{2a}{b}-1}}$
 [/INST] 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 $$2a-b\geq 0$$
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