In a given circuit, the total resistance is defined as

$\displaystyle {R}{T}={R}{1}+\frac{{{R}{2}\cdot{R}{3}}}{{{R}{2}+{R}{3}}}$ where R1, R2 and R3 are readings of three resistors.

Find the total resistance of a circuit with resistor #1 reading $\displaystyle \frac{{1}}{{10}}$ ohms, resistor #2 reading $\displaystyle \frac{{1}}{{4}}$ ohms, and resistor #3 reading $\displaystyle \frac{{1}}{{6}}$ ohms.

Give your answer as a fraction, reduced to lowest terms. No need to enter "ohms".