Answer
$x=\dfrac{yz}{z-y}$
Work Step by Step
By multiplying both sides by the $LCD=
xyz
$, the given equation, $
\dfrac{1}{x}=\dfrac{1}{y}-\dfrac{1}{z}
,$ is equivalent to
\begin{array}{l}\require{cancel}
yz(1)=xz(1)-xy(1)
\\\\
yz=xz-xy
.\end{array}
Using the properties of equality, then, in terms of $
x
,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
yz=x(z-y)
\\\\
\dfrac{yz}{z-y}=x
\\\\
x=\dfrac{yz}{z-y}
.\end{array}
