Answer
$x =\dfrac{abc}{b+a}$
Work Step by Step
Multiply $ab$ to both sides of the equation to obtain:
$\begin{array}{ccc}
\require{cancel}
&ab\left(\dfrac{x}{a} + \dfrac{x}{b}\right)&=&c(ab)
\\&\cancel{a}b\left(\dfrac{x}{\cancel{a}}\right) + a\cancel{b}\left(\dfrac{x}{\cancel{b}}\right)&=&abc
\\&bx+ax&=&abc
\end{array}$
Factor out $x$ to obtain:
$(b+a)x=abc$
Divide $(b+a)$ to both sides of the equation to obtain:
$x =\dfrac{abc}{b+a}$
