u = 30
continuing your method
[tex]\frac{1}{10}[/tex] = [tex]\frac{1}{u}[/tex] + [tex]\frac{1}{15}[/tex]
subtract [tex]\frac{1}{15}[/tex] from both sides
[tex]\frac{1}{u}[/tex] = [tex]\frac{1}{10}[/tex] - [tex]\frac{1}{15}[/tex] thus
[tex]\frac{1}{u}[/tex] = [tex]\frac{3}{30}[/tex] - [tex]\frac{2}{30}[/tex]
[tex]\frac{1}{u}[/tex] = [tex]\frac{1}{30}[/tex] ⇒ u = 30
