Answer
$x=\dfrac{21}{17}$
Work Step by Step
Substituting the given values in the given formula, then
\begin{array}{l}\require{cancel}
\dfrac{1}{x}=\dfrac{1}{y}+\dfrac{1}{z}-\dfrac{1}{w}
\\\\
\dfrac{1}{x}=\dfrac{1}{2}+\dfrac{1}{7}-\dfrac{1}{6}
.\end{array}
Using the $LCD=42x$ and the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
42x\left(\dfrac{1}{x}\right)=\left(\dfrac{1}{2}+\dfrac{1}{7}-\dfrac{1}{6}\right)42x
\\\\
42(1)=21x(1)+6x(1)+7x(1)
\\\\
42=21x+6x+7x
\\\\
42=34x
\\\\
\dfrac{42}{34}=x
\\\\
x=\dfrac{21}{17}
.\end{array}
