$u=\frac{A \sqrt{x}}{x+B}$

By the principle of homogeneity, $x=B$ (dimensionally)

$\Rightarrow B=[L]$

$\text { and }\left[ ML ^2 T ^{-2}\right]=\frac{A L^{1 / 2}}{L}$

${\left[ ML ^2 T ^{-2}\right]=A L^{-1 / 2}}$

$A=\left[ ML ^{3 / 2} T ^{-2}\right]$