$$-\frac{1}{R_{T}}=\frac{1}{5}+\frac{1}{10}+\frac{1}{15}$$
$R_{T} = -\frac{30}{11} = -2\frac{8}{11} \approx -2.727272727$
$$-30=30R_{T}\times \frac{1}{5}+30R_{T}\times \frac{1}{10}+30R_{T}\times \frac{1}{15}$$
$$-30=\frac{30}{5}R_{T}+30R_{T}\times \frac{1}{10}+30R_{T}\times \frac{1}{15}$$
$$-30=6R_{T}+30R_{T}\times \frac{1}{10}+30R_{T}\times \frac{1}{15}$$
$$-30=6R_{T}+\frac{30}{10}R_{T}+30R_{T}\times \frac{1}{15}$$
$$-30=6R_{T}+3R_{T}+30R_{T}\times \frac{1}{15}$$
$$-30=9R_{T}+30R_{T}\times \frac{1}{15}$$
$$-30=9R_{T}+\frac{30}{15}R_{T}$$
$$-30=9R_{T}+2R_{T}$$
$$-30=11R_{T}$$
$$11R_{T}=-30$$
$$R_{T}=\frac{-30}{11}$$
$$R_{T}=-\frac{30}{11}$$
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