Evaluate: (w-2)/(w)=(3)/(6)

Expression: $\frac{ w-2 }{ w }=\frac{ 3 }{ 6 }$

Determine the defined range

$\begin{array} { l }\frac{ w-2 }{ w }=\frac{ 3 }{ 6 },& w≠0\end{array}$

Cancel out the common factor $3$

$\frac{ w-2 }{ w }=\frac{ 1 }{ 2 }$

Simplify the equation using cross-multiplication

$2\left( w-2 \right)=w$

Distribute $2$ through the parentheses

$2w-4=w$

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

$2w=w+4$

Move the variable to the left-hand side and change its sign

$2w-w=4$

Collect like terms

$\begin{array} { l }w=4,& w≠0\end{array}$

Check if the solution is in the defined range

$w=4$