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Simplify stuck in simple expression


Hi - I wonder why

Simplify[(2 - Sqrt[72*(1+a*b)^2+4])/(2*a)];

in v. 4.2 gets stuck. It does not reduce the expression to 

(1 - Sqrt[18*(1+a*b)^2+1])/a;

FullSimplify and declaring-variable-attribute variations do not 
work.   What is necessary for the simplification to happen?


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