You didn't distribute when you multiplied the numerator by $\displaystyle\sqrt{{{b}}}\usepackage{cmbright}\Huge\$ . The first two steps are:

$\displaystyle\frac{{{3}+\sqrt{{b}}}}{{{3}\sqrt{{{b}}}}}\cdot\frac{\sqrt{{{b}}}}{\sqrt{{{b}}}}=\frac{{{3}\sqrt{{{b}}}+\sqrt{{{{b}}^{{2}}}}}}{{{3}\sqrt{{{{b}}^{{2}}}}}}\usepackage{cmbright}\Huge\$