<s>[INST] How do I simplify $\frac{bH}{a\sqrt{a^2+H^2}}$ to $\frac{b}{a\sqrt{a^2H^{-2}+1}}$?  
I have trouble following the algebraic simplification between step 2 and 3. 

How do I simplify $\frac{bH}{a\sqrt{a^2+H^2}}$ to $\frac{b}{a\sqrt{a^2H^{-2}+1}}$?

 [/INST] There you go
$$\frac{bH}{a\sqrt{a^2+H^2}}$$
$$=\frac{bH}{a\sqrt{(H^2)(\frac{a^2}{H^2}+1)}}$$
$$=\frac{bH}{aH\sqrt{\frac{a^2}{H^2}+1}}$$
$$=\frac{b}{a\sqrt{a^2H^{-2}+1}}$$
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