Answer
$x=\dfrac{abc}{a+b}$
Work Step by Step
Multiply both sides by $ab$.
$ab\left ( \dfrac{x}{a} + \dfrac{x}{b}\right )=ab\cdot c$
Use distributive property.
$ab\left ( \dfrac{x}{a} \right )+ ab\left ( \dfrac{x}{b}\right )=ab c$
Cancel common factors.
$bx+ ax=ab c$
Factor out $x$.
$x(b+ a)=ab c$
Divide both sides by $b+a$.
$\dfrac{x(b+a)}{b+a}=\dfrac{abc}{b+a}$
Simplify.
$x=\dfrac{abc}{a+b}$
