Calculate: (1)/(3)+(4)/(x)=(5)/(6)

Expression: $\frac{ 1 }{ 3 }+\frac{ 4 }{ x }=\frac{ 5 }{ 6 }$

Determine the defined range

$\begin{array} { l }\frac{ 1 }{ 3 }+\frac{ 4 }{ x }=\frac{ 5 }{ 6 },& x≠0\end{array}$

Move the constant to the right-hand side and change its sign

$\frac{ 4 }{ x }=\frac{ 5 }{ 6 }-\frac{ 1 }{ 3 }$

Subtract the fractions

$\frac{ 4 }{ x }=\frac{ 1 }{ 2 }$

Simplify the equation using cross-multiplication

$8=x$

Swap the sides of the equation

$\begin{array} { l }x=8,& x≠0\end{array}$

Check if the solution is in the defined range

$x=8$