Answer
$R_{eq}=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}}$
Work Step by Step
The equivalent resistance of two resistors connected in parallel is given by the following the expression:
$R_{eq}=\dfrac{1}{\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}}$
Evaluate the sum indicated in the denominator:
$\dfrac{1}{\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}}=\dfrac{1}{\dfrac{R_{2}+R_{1}}{R_{1}R_{2}}}=...$
Evaluate the division and simplify:
$...=1\div\dfrac{R_{1}+R_{2}}{R_{1}R_{2}}=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}}$
This simplified expression represents the equivalent resistance of two resistors in parallel:
$R_{eq}=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}}$
