Question

$$\frac{1}{c_{T}}=\frac{1}{c_{1}+c_{2}}+\frac{1}{c_{3}}$$

Solve for c_1

$c_{1}=-\frac{c_{3}c_{T}+c_{2}c_{T}-c_{2}c_{3}}{c_{T}-c_{3}}$
$c_{3}\neq 0\text{ and }c_{T}\neq 0\text{ and }c_{T}\neq c_{3}$

Solve for c_2

$c_{2}=-\frac{c_{3}c_{T}+c_{1}c_{T}-c_{1}c_{3}}{c_{T}-c_{3}}$
$c_{3}\neq 0\text{ and }c_{T}\neq 0\text{ and }c_{T}\neq c_{3}$