Calculate: (3)/(a)+(a-6)/(2a)-(1)/(3)

Expression: $\frac{ 3 }{ a }+\frac{ a-6 }{ 2a }-\frac{ 1 }{ 3 }$

Write all numerators above the least common denominator $6a$

$\frac{ 18+3\left( a-6 \right)-2a }{ 6a }$

Distribute $3$ through the parentheses

$\frac{ 18+3a-18-2a }{ 6a }$

Since two opposites add up to $0$, remove them from the expression

$\frac{ 3a-2a }{ 6a }$

Collect like terms

$\frac{ a }{ 6a }$

Cancel out the common factor $a$

$\begin{align*}&\frac{ 1 }{ 6 } \\&\begin{array} { l }0.1\overset{ \cdot }{ 6 } ,& {6}^{-1}\end{array}\end{align*}$